Relevant bibliographies by topics / Variety of algebra

Academic literature on the topic 'Variety of algebra'

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Published: 9 March 2023

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Journal articles on the topic "Variety of algebra"

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GIVANT, STEVEN, and HAJNAL ANDRÉKA. "THE VARIETY OF COSET RELATION ALGEBRAS." Journal of Symbolic Logic 83, no. 04 (December 2018): 1595–609. http://dx.doi.org/10.1017/jsl.2018.48.

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AbstractGivant [6] generalized the notion of an atomic pair-dense relation algebra from Maddux [13] by defining the notion of a measurable relation algebra, that is to say, a relation algebra in which the identity element is a sum of atoms that can be measured in the sense that the “size” of each such atom can be defined in an intuitive and reasonable way (within the framework of the first-order theory of relation algebras). In Andréka--Givant [2], a large class of examples of such algebras is constructed from systems of groups, coordinated systems of isomorphisms between quotients of the groups, and systems of cosets that are used to “shift” the operation of relative multiplication. In Givant--Andréka [8], it is shown that the class of these full coset relation algebras is adequate to the task of describing all measurable relation algebras in the sense that every atomic and complete measurable relation algebra is isomorphic to a full coset relation algebra.Call an algebra $\mathfrak{A}$ a coset relation algebra if $\mathfrak{A}$ is embeddable into some full coset relation algebra. In the present article, it is shown that the class of coset relation algebras is equationally axiomatizable (that is to say, it is a variety), but that no finite set of sentences suffices to axiomatize the class (that is to say, the class is not finitely axiomatizable).
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Padmanabhan, R., and P. Penner. "A Universal Variety of Point Algebras." Algebra Colloquium 17, no. 04 (December 2010): 647–58. http://dx.doi.org/10.1142/s1005386710000623.

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Point algebras introduced by Evans are algebraic systems which capture the essence of multiplications (a,b) · (c,d)=(p,q) defined on the set of all ordered pairs of elements of a set S, where p and q are selected from among a,b,c,d by some well-defined rule. In 1961, Jonsson and Tarski gave an interesting example of a variety of algebras of type 〈2,1,1〉 for illustrating the failure of certain free algebra properties. In this paper, we show that this equational class of algebras, called the JT-variety, is a universal variety of point algebras in the sense that every variety generated by a point algebra is a reduct of the JT-variety.
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Dziobiak, Wieslaw. "The subvariety lattice of the variety of distributive double p-algebras." Bulletin of the Australian Mathematical Society 31, no. 3 (June 1985): 377–87. http://dx.doi.org/10.1017/s0004972700009345.

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Let L denote the subvariety lattice of the variety of distributive double p-algebras, that is, the lattice whose universe consists of all varieties of distributive double p-algebras and whose ordering is the inclusion relation. We prove in this paper that each proper filter in L is uncountable. Moreover, we prove that except for the trivial variety (the zero in L) and the variety of Boolean algebras (the unique atom in L) every other element of L, generated by a finite algebra, has infinitely many covers in L, among which at least one is not generated by any finite algebra. The former result strengthens a result of Urquhart who showed that the lattice L is uncountable. On the other hand, both of our results indicate a high complexity of the lattice L at least in comparison with the subvariety lattice of the variety of distributive p-algebras, since a result of Lee shows that the latter lattice forms a chain of type ω + 1 and every cover in it of the variety generated by a finite algebra is itself generated by a finite algebra.
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Benanti, Francesca, Onofrio M. Di Vincenzo, and Vincenzo Nardozza. "*-Subvarieties of the Variety Generated by." Canadian Journal of Mathematics 55, no. 1 (February 1, 2003): 42–63. http://dx.doi.org/10.4153/cjm-2003-002-7.

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AbstractLet be a field of characteristic zero, and * = t the transpose involution for the matrix algebra M2(). Let be a proper subvariety of the variety of algebras with involution generated by . We define two sequences of algebras with involution Rp, Sq, where p, q ∊ . Then we show that T*() and T*(Rp ⊕ Sq) are *-asymptotically equivalent for suitable p, q.
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Remm, Elisabeth. "3-Dimensional Skew-symmetric Algebras and the Variety of Hom-Lie Algebras." Algebra Colloquium 25, no. 04 (December 2018): 547–66. http://dx.doi.org/10.1142/s100538671800038x.

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An algebra is called skew-symmetric if its multiplication operation is a skewsymmetric bilinear application. We determine all these algebras in dimension 3 over a field of characteristic different from 2. As an application, we determine the subvariety of 3-dimensional Hom-Lie algebras. For this type of algebra, we study also the case of dimension 4.
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Chen, Cong. "The nilpotent variety of W(1;n)p is irreducible." Journal of Algebra and Its Applications 18, no. 03 (March 2019): 1950056. http://dx.doi.org/10.1142/s0219498819500567.

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In the late 1980s, Premet conjectured that the nilpotent variety of any finite dimensional restricted Lie algebra over an algebraically closed field of characteristic [Formula: see text] is irreducible. This conjecture remains open, but it is known to hold for a large class of simple restricted Lie algebras, e.g. for Lie algebras of connected algebraic groups, and for Cartan series [Formula: see text] and [Formula: see text]. In this paper, with the assumption that [Formula: see text], we confirm this conjecture for the minimal [Formula: see text]-envelope [Formula: see text] of the Zassenhaus algebra [Formula: see text] for all [Formula: see text].
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KHARLAMPOVICH, O., and D. GILDENHUYS. "THE WORD PROBLEM FOR SOME VARIETIES OF SOLVABLE LIE ALGEBRAS." International Journal of Algebra and Computation 04, no. 03 (September 1994): 481–91. http://dx.doi.org/10.1142/s0218196794000117.

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The word problem is said to be solvable in a variety of Lie algebras if it is solvable in every algebra, finitely presented in this variety. Let [Formula: see text] denote the variety of (2-step nilpotent)-by-abelian Lie algebra and [Formula: see text] the variety of abelian-by-(2-step nilpotent) Lie algebras. It is proved that the word problem is unsolvable in the “interval” of varieties containing the variety [Formula: see text] (of centre-by-[Formula: see text] Lie algebras over a field of characteristic zero), and contained in the variety [Formula: see text].
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MIKHALEV, ALEXANDER A., and JIE-TAI YU. "STABLE EQUIVALENCE PROBLEMS FOR FREE ALGEBRAS WITH THE NIELSEN-SCHREIER PROPERTY." International Journal of Algebra and Computation 11, no. 06 (December 2001): 779–86. http://dx.doi.org/10.1142/s0218196701000747.

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A variety of algebras is said to be Schreier if any subalgebra of a free algebra of this variety is free in the same variety of algebras. For free algebras of finite ranks of Schreier varieties we prove that if two systems of elements are stably equivalent, then they are equivalent. We define the rank of an endomorphism of a free algebra of a Schreier variety and prove that an injective endomorphism of maximal rank does not change the rank of elements of maximal rank.
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Abad, M., and J. P. Díaz Varela. "Free algebras in the variety of three-valued closure algebras." Journal of the Australian Mathematical Society 72, no. 2 (April 2002): 181–98. http://dx.doi.org/10.1017/s1446788700003839.

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AbstractIn this paper, the variety of three-valued closure algebras, that is, closure algebras with the property that the open elements from a three-valued Heyting algebra, is investigated. Particularly, the structure of the finitely generated free objects in this variety is determined.
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BLOOM, STEPHEN L., and ZOLTÁN ÉSIK. "Varieties generated by languages with poset operations." Mathematical Structures in Computer Science 7, no. 6 (December 1997): 701–13. http://dx.doi.org/10.1017/s0960129597002442.

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A V-labelled poset P can induce an operation on the languages on any fixed alphabet, as well as an operation on labelled posets (as noticed by Pratt and Gischer (Pratt 1986; Gischer 1988)). For any collection X of V-labelled posets and any alphabet Σ we obtain an X-algebra ΣX of languages on Σ. We consider the variety Lang(X) generated by these algebras when X is a collection of nonempty ‘traceable posets’. The current paper contains several observations about this variety. First, we use one of the basic results in Bloom and Ésik (1996) to show that a concrete description of the A-generated free algebra in Lang(X) is the X-subalgebra generated by the singletons (labelled a∈A) in the X-algebra of all A-labelled posets. Equipped with an appropriate ordering, these same algebras are the free ordered algebras in the variety Lang(X)[les ] of ordered language X-algebras. Further, if one enriches the language algebras by adding either a binary or infinitary union operation, the free algebras in the resulting variety are described by certain ‘closed’ subsets of the original free algebras. Second, we show that for ‘reasonable sets’ X, the variety Lang(X) has the property that for each n[ges ]2, the n-generated free algebra is a subalgebra of the 1-generated free algebra. Third, knowing the free algebras enables us to show that these varieties are generated by the finite languages on a two-letter alphabet.
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Dissertations / Theses on the topic "Variety of algebra"

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Lundqvist, Samuel. "Computational algorithms for algebras." Doctoral thesis, Stockholm : Department of Mathematics, Stockholm University, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-31552.

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Diss. (sammanfattning) Stockholm : Stockholms universitet, 2009.
At the time of doctoral defence, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript. Paper 5: Manuscript. Paper 6: Manuscript. Härtill 6 uppsatser.
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TSAKIRIS, MANOLIS. "On resolutions of ideals associated to subspace arrangements and the algebraic matroid of the determinantal variety." Doctoral thesis, Università degli studi di Genova, 2021. http://hdl.handle.net/11567/1045090.

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THIS THESIS DESCRIBES THE GRADED MINIMAL FREE RESOLUTION OF A PRODUCT OF IDEALS, EACH GENERATED BY LINEAR FORMS. IT ALSO STUDIES A PHENOMENON OF LINEARIZATION OF THE RESOLUTION OF AN ARBITRARY IDEAL, UPON MULTIPLICATION BY SUFFICIENTLY MANY IDEALS OF GENERIC POINTS IN PROJECTIVE SPACE. FURTHER, IT PROVIDES A CLASS OF BASE SETS OF THE ALGEBRAIC MATROID OF THE DETERMINANTAL VARIETY AND CONJECTURES THAT THESE COMPLETELY CHARACTERIZE THE MATROID. FINALLY, IT PROVIDES DETERMINANTAL CONDITIONS FOR HOMOMORPHIC SENSING, A PROBLEM THAT STUDIES THE UNIQUENESS OF IMAGES OF POINTS IN A VECTOR SUBSPACE UNDER A FINITE SET OF LINEAR TRANSFORMATIONS.
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Lemay, Joel. "Geometric Realizations of the Basic Representation of the Affine General Linear Lie Algebra." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32866.

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The realizations of the basic representation of the affine general linear Lie algebra on (r x r) matrices are well-known to be parametrized by partitions of r and have an explicit description in terms of vertex operators on the bosonic/fermionic Fock space. In this thesis, we give a geometric interpretation of these realizations in terms of geometric operators acting on the equivariant cohomology of certain Nakajima quiver varieties.
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Sistko, Alexander Harris. "Maximal subalgebras of finite-dimensional algebras: with connections to representation theory and geometry." Diss., University of Iowa, 2019. https://ir.uiowa.edu/etd/6857.

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Let $k$ be a field and $B$ a finite-dimensional, associative, unital $k$-algebra. For each $1 \le d \le \dim_kB$, let $\operatorname{AlgGr}_d(B)$ denote the projective variety of $d$-dimensional subalgebras of $B$, and let $\operatorname{Aut}_k(B)$ denote the automorphism group of $B$. In this thesis, we are primarily concerned with understanding the relationship between $\operatorname{AlgGr}_d(B)$, the representation theory of $B$, and the representation theory of $\operatorname{Aut}_k(B)$. We begin by proving fundamental structure theorems for the maximal subalgebras of $B$. We show that maximal subalgebras of $B$ come in two flavors, which we call split type and separable type. As a consequence, we provide complete classifications for maximal subalgebras of semisimple algebras and basic algebras. We also demonstrate that the maximality of $A$ in $B$ is related to the representation theory of $B$, through the separability of functors closely associated with the extension $A \subset B$. The rest of this document showcases applications of these results. For $k = \bar{k}$, we compute the maximal dimension of a proper subalgebra of $B$. We discuss the problem of computing the minimal number of generators for $B$ (as an algebra), and provide upper and lower bounds for basic algebras. We then study $\operatorname{AlgGr}_d(B)$ in detail, again when $B$ is basic. When $d = \dim_kB-1$, we find a projective embedding of $\operatorname{AlgGr}_d(B)$, and explicitly describe its associated homogeneous vanishing ideal. In turn, we provide a simple description of its irreducible components. We find equivalent conditions for this variety to be a finite union of $\operatorname{Aut}_k(B)$-orbits, and describe several classes of algebras which satisfy these conditions. Furthermore, we provide an algebraic description for the orbits of connected maximal subalgebras of type-$\mathbb{A}$ path algebras. Finally, we study the fixed-point variety $\operatorname{AlgGr}_d(B)^{\operatorname{Aut}_k(B)}$ (for general $d$), which connects naturally to the representation theory of $\operatorname{Aut}_k(B)$. We investigate the case where $B$ is a truncated path algebra over $\mathbb{C}$ in detail.
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Fujita, Ryo. "A geometric study of Dynkin quiver type quantum affine Schur-Weyl duality." Kyoto University, 2019. http://hdl.handle.net/2433/242573.

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ABBADINI, MARCO. "ON THE AXIOMATISABILITY OF THE DUAL OF COMPACT ORDERED SPACES." Doctoral thesis, Università degli Studi di Milano, 2021. http://hdl.handle.net/2434/812809.

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We prove that the category of Nachbin's compact ordered spaces and order-preserving continuous maps between them is dually equivalent to a variety of algebras, with operations of at most countable arity. Furthermore, we show that the countable bound on the arity is the best possible: the category of compact ordered spaces is not dually equivalent to any variety of finitary algebras. Indeed, the following stronger results hold: the category of compact ordered spaces is not dually equivalent to (i) any finitely accessible category, (ii) any first-order definable class of structures, (iii) any class of finitary algebras closed under products and subalgebras. An explicit equational axiomatisation of the dual of the category of compact ordered spaces is obtained; in fact, we provide a finite one, meaning that our description uses only finitely many function symbols and finitely many equational axioms. In preparation for the latter result, we establish a generalisation of a celebrated theorem by D. Mundici: our result asserts that the category of unital commutative distributive lattice-ordered monoids is equivalent to the category of what we call MV-monoidal algebras. Our proof is independent of Mundici's theorem.
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Gawell, Elin. "Centra of Quiver Algebras." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-106734.

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A partly (anti-)commutative quiver algebra is a quiver algebra bound by an (anti-)commutativity ideal, that is, a quadratic ideal generated by monomials and (anti-)commutativity relations. We give a combinatorial description of the ideals and the associated generator graphs, from which one can quickly determine if the ideal is admissible or not. We describe the center of a partly (anti-)commutative quiveralgebra and state necessary and sufficient conditions for the center to be finitely genteratedas a K-algebra.Examples are provided of partly (anti-)commutative quiver algebras that are Koszul algebras. Necessary and sufficient conditions for finite generation of the Hochschild cohomology ring modulo nilpotent elements for a partly (anti-)commutative Koszul quiver algebra are given.
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Bittencourt, Vinicius Souza. "Variedades não matriciais em certas classes de álgebras não associativas." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-29082016-211053/.

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Uma variedade M de álgebras associativas é dita ser não matricial se F² não está em M, em que F² é o anel das matrizes quadradas de ordem 2 sobre F. Latyshev introduziu estas variedades em 1977. A respeito desta definição, outras caracterizações equivalentes para uma variedade não matricial foram obtidas, por exemplo, ao considerar elementos algébricos (Cekanu, 1979) e nilpotentes (Mishckenko et al, 2011). Variedades não matriciais são estudadas principalmente no caso sobre os corpos de característica zero para álgebras associativas. A teoria geral de variedades de álgebras, entretanto, não está restrita à classe das álgebras associativas. Além das álgebras de Lie, entre as muitas classes de álgebras não associativas, nós destacamos as álgebras alternativas, as de Jordan e as de Jordan não comutativas. Estas classes de álgebras têm muitas conexões e aplicações a diversas áreas da Matemática e da Física e têm uma teoria estrutural bem desenvolvida, assim como a classe das álgebras associativas. O conceito de variedade não matricial pode ser reformulado para as classes de álgebras supracitadas e nosso trabalho consiste em adaptar, estender ou generalizar alguns resultados, conforme mencionado, para variedades não matriciais nestas classes de álgebras.
A variety M of associative algebras (over a field F) is called ``nonmatrix\'\' if F² is not in M, where F² is the usual matrix algebra of second order over F. Latyshev introduced these varieties in 1977. Concerning this definition, other equivalent characterizations for a nonmatrix variety were obtained, for instance, by considering algebraic (Cekanu, 79) and nilpotent (Mishchenko et all, 2011) elements. Non-matrix varieties are studied mainly in the case of characteristic zero for associative algebras. However, the general theory of varieties of algebras is not restricted to the class of associative algebras. In addition to the Lie algebras, among many classes of non associative algebras, we highlight the alternative, the Jordan and the non commutative Jordan algebras. These classes of algebras have many connexions and applications to several areas of Mathematics and Physics and have a well-developed structural theory, as in the class of associative algebras. The concept of ``nonmatrix variety\'\' can be reformulated in the classes of algebras above and our work is to adapt, extend or generalize some results, as mentioned, for non-matrix varieties in these classes of algebras.
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Rovi, Carmen. "Algebraic Curves over Finite Fields." Thesis, Linköping University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-56761.

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This thesis surveys the issue of finding rational points on algebraic curves over finite fields. Since Goppa's construction of algebraic geometric codes, there has been great interest in finding curves with many rational points. Here we explain the main tools for finding rational points on a curve over a nite eld and provide the necessary background on ring and field theory. Four different articles are analyzed, the first of these articles gives a complete set of table showing the numbers of rational points for curves with genus up to 50. The other articles provide interesting constructions of covering curves: covers by the Hemitian curve, Kummer extensions and Artin-Schreier extensions. With these articles the great difficulty of finding explicit equations for curves with many rational points is overcome. With the method given by Arnaldo García in [6] we have been able to nd examples that can be used to define the lower bounds for the corresponding entries in the tables given in http: //wins.uva.nl/~geer, which to the time of writing this Thesis appear as "no information available". In fact, as the curves found are maximal, these entries no longer need a bound, they can be given by a unique entry, since the exact value of Nq(g) is now known.

At the end of the thesis an outline of the construction of Goppa codes is given and the NXL and XNL codes are presented.

 

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V, Budimirović Branka. "Mrežno vrednosni identiteti i neke klase mrežno vrednosnih podalgebri." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2011. https://www.cris.uns.ac.rs/record.jsf?recordId=77334&source=NDLTD&language=en.

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Neka je A neprazan skup i L = (L;·) proizvoljna mreža sa nulom i jedinicom. Svako preslikavanje A¯ : A ¡! L zovemo rasplinuti podskup od A. Uobičajeno je da se rasplinute podgrupe definišu na grupi. U radu su fazi podgrupe definisane na polugrupi kao i na rasplinutoj podpolugrupi. Jedan od glavnih rezultata je teorema o particiji rasplinutih kompletno regularnih polugrupa. Takođe su definisane rasplinute kongruencije i rasplinute jednakosti na rasplinutim podalgebrama neke algebre i ispitane njihove osobine. Uvedeni su pojmovi: podalgebre rasplinute podalgebre, rasplinutog homomorfizma rasplinute podalgebre na rasplinutu podalgebru i direktnog proizvoda rasplinutih podalgebri. Jedan od važnijih rezultata je teorema koja je uopštenje teoreme Birkhoff-a na rasplinutim strukturama.
Let A be nonemptu set, and let L = (L; 6) be a lattice with 0 and 1. The mapping A¯ : A ! L is called fuzzy subset of A. It is usual to define fuzzy subgroup on the group. In this work fuzzy semigroups are defined on the semigroup and on the fuzzy subsemigroup, too. As a main result is theorem about partition fuzzy completlu regular semigroup. Also, fuzzy congruences are defined, and fuzzy equolites on fuzzy subalgebras of an algebra and their propertes are investigated. We introduced some new notions: subalgebras of fuzzy subalgebras, fuzzy homomorphism of fuzzy subalgebra, and direct product of fuzzy subalgebras. One of the most important result is extension of Birkhoff’s theorem on fuzzy structures.
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Books on the topic "Variety of algebra"

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1938-, Griffiths Phillip, ed. On the tangent space to the space of algebraic cycles on a smooth algebraic variety. Princeton, N.J: Princeton University Press, 2004.

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Quantitative arithmetic of projective varieties. Basel: Birkhäuser, 2009.

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J, Kovacs Sandor, ed. Classification of higher dimensional algebraic varieties. Basel: Birkhäuser, 2010.

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Bjorn, Poonen, and Tschinkel Yuri, eds. Arithmetic of higher-dimensional algebraic varieties. Boston: Birkhäuser, 2004.

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Johnsen, Trygve. K3 Projective models in scrolls. Berlin: Springer, 2004.

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Johnsen, Trygve. K3 Projective models in scrolls. Berlin: Springer, 2004.

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Voisin, Claire. Théorie de Hodge et géométrie algébrique complexe. Paris: Société Mathématique de France, 2002.

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Introduction to Algebra with Applications for a Variety of Technologies. 3rd ed. Kendall/Hunt Publishing Company, 2002.

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Hart, Jerome B., and Roxane R. Barrows. Introduction to Algebra with Applications for a Variety of Technologies. 2nd ed. Kendall/Hunt Publishing Company, 1999.

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Bushko, Andrew. Introduction to Algebra with Applications for a Variety of Technologies. Kendall/Hunt Publishing Company, 1998.

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Book chapters on the topic "Variety of algebra"

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de la Concepción, Daniel, and Abdenacer Makhlouf. "Variety of Hom-Sabinin Algebras and Related Algebra Subclasses." In Springer Proceedings in Mathematics & Statistics, 25–49. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-78346-4_3.

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Hida, Haruzo. "Invariants, Shimura Variety, and Hecke Algebra." In Springer Monographs in Mathematics, 83–144. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6657-4_3.

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Grigoriev, Dima. "Polynomial Complexity Recognizing a Tropical Linear Variety." In Computer Algebra in Scientific Computing, 152–57. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24021-3_11.

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Nester, Chad. "A Variety Theorem for Relational Universal Algebra." In Relational and Algebraic Methods in Computer Science, 362–77. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-88701-8_22.

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Miró-Roig, Rosa M. "Lectures on the Representation Type of a Projective Variety." In Commutative Algebra and its Interactions to Algebraic Geometry, 165–216. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75565-6_3.

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Kunz, Ernst. "On the number of equations needed to describe an algebraic variety." In Introduction to Commutative Algebra and Algebraic Geometry, 123–62. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4612-5290-0_5.

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Kunz, Ernst. "On the number of equations needed to describe an algebraic variety." In Introduction to Commutative Algebra and Algebraic Geometry, 123–62. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-5987-3_5.

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Valkenburg, Robert, and Leo Dorst. "Estimating Motors from a Variety of Geometric Data in 3D Conformal Geometric Algebra." In Guide to Geometric Algebra in Practice, 25–45. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-811-9_2.

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McNulty, George F. "The computational complexity of deciding whether a finite algebra generates a minimal variety." In Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science, 233–56. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74772-9_9.

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Boisseau, Guillaume, and Robin Piedeleu. "Graphical Piecewise-Linear Algebra." In Lecture Notes in Computer Science, 101–19. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99253-8_6.

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AbstractGraphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds of subsets of vector spaces compositionally. It has been used to model various application domains, from signal-flow graphs to Petri nets and electrical circuits. In this paper, we introduce to the family its most expressive member to date: Graphical Piecewise-Linear Algebra, a new language to specify piecewise-linear subsets of vector spaces.Like the previous members of the family, it comes with a complete axiomatisation, which means it can be used to reason about the corresponding semantic domain purely equationally, forgetting the set-theoretic interpretation. We show completeness using a single axiom on top of Graphical Polyhedral Algebra, and show that this extension is the smallest that can capture a variety of relevant constructs.Finally, we showcase its use by modelling the behaviour of stateless electronic circuits of ideal elements, a domain that had remained outside the remit of previous diagrammatic languages.
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Conference papers on the topic "Variety of algebra"

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Zhang, Wen Ting, and Yan Feng Luo. "The Variety Generated by All Non-Permutative and Non-Idempotent Semigroups of Order Four." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0059.

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MOGHADDAM, MOHAMMAD REZA R., and ALI REZA SALEMKAR. "GENERALIZED SCHREIER VARIETY AND A CRITERION FOR NON-EXISTENCE OF COVERING GROUPS." In Proceedings of the ICM Satellite Conference in Algebra and Related Topics. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705808_0014.

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Di Nola, Antonio, and Tommaso Flaminio. "Generating the Variety of SMV-Algebras." In 2010 40th IEEE International Symposium on Multiple-Valued Logic. IEEE, 2010. http://dx.doi.org/10.1109/ismvl.2010.34.

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Jenei, Sandor, and Laszlo Korodi. "On the variety of equality algebras." In 7th conference of the European Society for Fuzzy Logic and Technology. Paris, France: Atlantis Press, 2011. http://dx.doi.org/10.2991/eusflat.2011.1.

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Gomes, Joel Felipe Ferreira, and Vitor Rodrigues Greati. "Notes on the Logic of Perfect Paradefinite Algebras." In Workshop Brasileiro de Lógica. Sociedade Brasileira de Computação, 2021. http://dx.doi.org/10.5753/wbl.2021.15777.

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This work introduces the variety of perfect paradefinite algebras (PPalgebras), consisting of De Morgan algebras enriched with a perfect operator o, which turns out to be equivalent to the variety of involutive Stone algebras (IS-algebras). The corresponding order-preserving logic PP≤ is a Logic of Formal Inconsistency, a Logic of Formal Undeterminedness, a C-system and a D-system, some of these features being evident in the proposed axiomatization of PP-algebras. After proving the mentioned algebraic equivalence, we show how to axiomatize, by means of Hilbert-style calculi, certain extensions of De Morgan algebras with a perfect operator and, in particular, the logic PP≤.
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Hossain, Awlad. "Teaching an Undergraduate Introductory Finite Element Analysis Course: Successful Implementation for Students Learning." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-50091.

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In our institution, we offer a one-quarter long finite element analysis (FEA) class for Mechanical Engineering curriculum. This course teaches computational methods to solve engineering problems using the state of art FEA software ANSYS. The coursework involves teaching fundamental mathematical theories to build the concept, analyzing simple structural problems using matrix algebra, and then solving a wide variety of engineering problems dealing with statics, dynamics, heat transfer and others. Students enrolled in this class solve varieties of problem by analytical approach, finite element approach using matrix algebra, using APDL (ANSYS Parametric Design Language) and ANSYS Workbench. As we are in quarter system, it is challenging to solve additional multidisciplinary complex engineering problems in regular class lectures. Therefore, students enrolled in this class are required to conduct a project solvable by student version of ANSYS within very short time. The project must have adequate engineering complexity conveying interesting knowledge or technical concepts to the entire class. Students have to prepare a brief written report, and share what they have learned with the entire class giving an oral presentation. While a course in FEA could be a common offering in many universities, the author of this paper presents the pedagogical approaches undertaken to successfully implement the course objectives to the undergraduate engineering students. The topics and techniques applied to teach different concepts of FEA to enhance students learning outcomes are addressed in this paper.
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Dmitrieva, Ilzina, Gennadiy Ivanov, and Alexey Mineev. "Geometric support of algorithms for solving Problems of higher mathematics." In International Conference "Computing for Physics and Technology - CPT2020". Bryansk State Technical University, 2020. http://dx.doi.org/10.30987/conferencearticle_5fce277310b6d4.05756248.

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The need to improve the level of mathematical in particular geometric training of students of technical universities is due to modern technologies of computer-aided design. They are based on mathematical models of designed products, technological processes, etc., taking into account a large variety of source data. Therefore, from the first years of technical universities, when studying the cycle of mathematical disciplines, it is advisable to interpret a number of issues in terms and concepts of multidimensional geometry. At the same time, the combination of constructive (graphical) algorithms for solving problems in descriptive geometry with analytical algorithms in linear algebra and matanalysis allows us to summarize their advantages: the constructive approach provides the imagery inherent in engineering thinking, and the analytical approach provides the final result. The article shows the effectiveness of combining constructive and analytical algorithms for solving problems involving linear and nonlinear forms of many variables using specific examples.
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Rosales, Marta B., and Carlos P. Filipich. "An Algebraic Series Method to Solve Strongly Nonlinear Oscillators." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-43983.

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The well-known technique of power series is exploited here to find a recurrence algorithm to solve strongly nonlinear oscillators. A wide variety of nonlinearities may be tackled with this approach. Simple recurrence relationship are obtained after some algebra handling. Three illustrations are analytically developed and numerically solved: a parametrically excited nonlinear oscillator, the differential equation of motion of a moored structure with non-truncated mooring nonlinearities and the classical Lorenz oscillator. In the first illustration a strongly nonlinear parametric oscillator that governs a rotor dynamics problem is solved. The results are depicted as trajectories, phase plots and Poincare´ maps. The second illustrations deals with the dynamic behavior of a simplified model of a small floating structure anchored by chains or cables. This type of structure is sometimes known as Catenary Anchor Leg Mooring (CALM) system. The structure is first modeled as a two DOF oscillator with strongly nonlinear stiffness and subjected to a harmonic wave force. A further simplification is introduced by prescribing the vertical motion as a harmonic oscillation. Then, the resulting equation is stated with a single DOF. Here the use of the power series is twofold: an algebraic recurrence algorithm is employed to obtain a nontruncated differential equation and, as in the first illustration, also used as a time integration scheme. When the forcing frequency is chosen as the bifurcation parameter, the system shows diverse type of solutions: 1-, 3-, multi-period, and quasiperiodic behavior. The third illustration deals with the well-known Lorenz system. The strange attractor is obtained without difficulties.
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Lima Neto, Clodomir Silva, Thiago Nascimento da Silva, and Umberto Rivieccio. "Quasi-N4-lattices and their logic." In Workshop Brasileiro de Lógica. Sociedade Brasileira de Computação, 2022. http://dx.doi.org/10.5753/wbl.2022.222852.

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The variety of quasi-N4-lattices (QN4) was recently introduced as a non-involutive generalization of N4-lattices (algebraic models of Nelson's paraconsistent logic). While research on these algebras is still at a preliminary stage, we know that QN4 is an arithmetical variety which possesses a ternary as well as a quaternary deductive term, enjoys equationally definable principal congruences and the strong congruence extension property. We furthermore have recently introduced an algebraizable logic having QN4 as its equivalent semantics. In this contribution we report on the results obtained so far on this class of algebras and on its logical counterpart.
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Jetton, Cole, Liam Rudd, and Matthew I. Campbell. "Systematic Generation of 5-Axis Manufacturing Machines." In ASME 2022 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/detc2022-87874.

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Abstract Additive and subtractive machines that exhibit five and six degrees of freedom are on the cutting edge of manufacturing technology. The workspace for these machines can be determined by the joint types and orientations chosen during the design process. Thus, many joint configurations should be considered during the design. This paper presents a method for exhaustively generating and evaluating serial mechanisms using computer algebra systems and investigates four machines as case studies. The position and angle of the end point of the mechanism was computed as a function of joint actuation allowing a configuration to be evaluated in a variety of metrics including volume, tool angle range, and singularities (where the machine loses a degree of freedom). The exhaustive search generated and tested joint configurations to determine which had five axis control within their workspace. The case studies looked at four machines in detail, using both convex hull and alpha shape to calculate the workspace volume, their ability to maintain five axis control, and compared the viability of each configuration. The application of this method led to several different, but viable configurations. One can then narrow down further based on situational requirements of the target environment.
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Reports on the topic "Variety of algebra"

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Abdellatif, Omar S., and Ali Behbehani. Algeria COVID-19 Governmental Response. UN Compliance Research Group, February 2021. http://dx.doi.org/10.52008/alg0501.

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The International Health Regulations (2005) are legally binding on 196 States Parties, Including all WHO Member States. The IHR aims to keep the world informed about public health risks, through committing all signatories to cooperate together in combating any future “illness or medical condition, irrespective of origin or source, that presents or could present significant harm to humans.” Under IHR, countries agreed to strengthen their public health capacities and notify the WHO of any such illness in their populations. The WHO would be the centralized body for all countries facing a health threat, with the power to declare a “public health emergency of international concern,” issue recommendations, and work with countries to tackle a crisis. Although, with the sudden and rapid spread of COVID-19 in the world, many countries varied in implementing the WHO guidelines and health recommendations. While some countries followed the WHO guidelines, others imposed travel restrictions against the WHO’s recommendations. Some refused to share their data with the organization. Others banned the export of medical equipment, even in the face of global shortages. The UN Compliance Research group will focus during the current cycle on analyzing the compliance of the WHO member states to the organizations guidelines during the COVID-19 pandemic.
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African Open Science Platform Part 1: Landscape Study. Academy of Science of South Africa (ASSAf), 2019. http://dx.doi.org/10.17159/assaf.2019/0047.

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This report maps the African landscape of Open Science – with a focus on Open Data as a sub-set of Open Science. Data to inform the landscape study were collected through a variety of methods, including surveys, desk research, engagement with a community of practice, networking with stakeholders, participation in conferences, case study presentations, and workshops hosted. Although the majority of African countries (35 of 54) demonstrates commitment to science through its investment in research and development (R&D), academies of science, ministries of science and technology, policies, recognition of research, and participation in the Science Granting Councils Initiative (SGCI), the following countries demonstrate the highest commitment and political willingness to invest in science: Botswana, Ethiopia, Kenya, Senegal, South Africa, Tanzania, and Uganda. In addition to existing policies in Science, Technology and Innovation (STI), the following countries have made progress towards Open Data policies: Botswana, Kenya, Madagascar, Mauritius, South Africa and Uganda. Only two African countries (Kenya and South Africa) at this stage contribute 0.8% of its GDP (Gross Domestic Product) to R&D (Research and Development), which is the closest to the AU’s (African Union’s) suggested 1%. Countries such as Lesotho and Madagascar ranked as 0%, while the R&D expenditure for 24 African countries is unknown. In addition to this, science globally has become fully dependent on stable ICT (Information and Communication Technologies) infrastructure, which includes connectivity/bandwidth, high performance computing facilities and data services. This is especially applicable since countries globally are finding themselves in the midst of the 4th Industrial Revolution (4IR), which is not only “about” data, but which “is” data. According to an article1 by Alan Marcus (2015) (Senior Director, Head of Information Technology and Telecommunications Industries, World Economic Forum), “At its core, data represents a post-industrial opportunity. Its uses have unprecedented complexity, velocity and global reach. As digital communications become ubiquitous, data will rule in a world where nearly everyone and everything is connected in real time. That will require a highly reliable, secure and available infrastructure at its core, and innovation at the edge.” Every industry is affected as part of this revolution – also science. An important component of the digital transformation is “trust” – people must be able to trust that governments and all other industries (including the science sector), adequately handle and protect their data. This requires accountability on a global level, and digital industries must embrace the change and go for a higher standard of protection. “This will reassure consumers and citizens, benefitting the whole digital economy”, says Marcus. A stable and secure information and communication technologies (ICT) infrastructure – currently provided by the National Research and Education Networks (NRENs) – is key to advance collaboration in science. The AfricaConnect2 project (AfricaConnect (2012–2014) and AfricaConnect2 (2016–2018)) through establishing connectivity between National Research and Education Networks (NRENs), is planning to roll out AfricaConnect3 by the end of 2019. The concern however is that selected African governments (with the exception of a few countries such as South Africa, Mozambique, Ethiopia and others) have low awareness of the impact the Internet has today on all societal levels, how much ICT (and the 4th Industrial Revolution) have affected research, and the added value an NREN can bring to higher education and research in addressing the respective needs, which is far more complex than simply providing connectivity. Apart from more commitment and investment in R&D, African governments – to become and remain part of the 4th Industrial Revolution – have no option other than to acknowledge and commit to the role NRENs play in advancing science towards addressing the SDG (Sustainable Development Goals). For successful collaboration and direction, it is fundamental that policies within one country are aligned with one another. Alignment on continental level is crucial for the future Pan-African African Open Science Platform to be successful. Both the HIPSSA ((Harmonization of ICT Policies in Sub-Saharan Africa)3 project and WATRA (the West Africa Telecommunications Regulators Assembly)4, have made progress towards the regulation of the telecom sector, and in particular of bottlenecks which curb the development of competition among ISPs. A study under HIPSSA identified potential bottlenecks in access at an affordable price to the international capacity of submarine cables and suggested means and tools used by regulators to remedy them. Work on the recommended measures and making them operational continues in collaboration with WATRA. In addition to sufficient bandwidth and connectivity, high-performance computing facilities and services in support of data sharing are also required. The South African National Integrated Cyberinfrastructure System5 (NICIS) has made great progress in planning and setting up a cyberinfrastructure ecosystem in support of collaborative science and data sharing. The regional Southern African Development Community6 (SADC) Cyber-infrastructure Framework provides a valuable roadmap towards high-speed Internet, developing human capacity and skills in ICT technologies, high- performance computing and more. The following countries have been identified as having high-performance computing facilities, some as a result of the Square Kilometre Array7 (SKA) partnership: Botswana, Ghana, Kenya, Madagascar, Mozambique, Mauritius, Namibia, South Africa, Tunisia, and Zambia. More and more NRENs – especially the Level 6 NRENs 8 (Algeria, Egypt, Kenya, South Africa, and recently Zambia) – are exploring offering additional services; also in support of data sharing and transfer. The following NRENs already allow for running data-intensive applications and sharing of high-end computing assets, bio-modelling and computation on high-performance/ supercomputers: KENET (Kenya), TENET (South Africa), RENU (Uganda), ZAMREN (Zambia), EUN (Egypt) and ARN (Algeria). Fifteen higher education training institutions from eight African countries (Botswana, Benin, Kenya, Nigeria, Rwanda, South Africa, Sudan, and Tanzania) have been identified as offering formal courses on data science. In addition to formal degrees, a number of international short courses have been developed and free international online courses are also available as an option to build capacity and integrate as part of curricula. The small number of higher education or research intensive institutions offering data science is however insufficient, and there is a desperate need for more training in data science. The CODATA-RDA Schools of Research Data Science aim at addressing the continental need for foundational data skills across all disciplines, along with training conducted by The Carpentries 9 programme (specifically Data Carpentry 10 ). Thus far, CODATA-RDA schools in collaboration with AOSP, integrating content from Data Carpentry, were presented in Rwanda (in 2018), and during17-29 June 2019, in Ethiopia. Awareness regarding Open Science (including Open Data) is evident through the 12 Open Science-related Open Access/Open Data/Open Science declarations and agreements endorsed or signed by African governments; 200 Open Access journals from Africa registered on the Directory of Open Access Journals (DOAJ); 174 Open Access institutional research repositories registered on openDOAR (Directory of Open Access Repositories); 33 Open Access/Open Science policies registered on ROARMAP (Registry of Open Access Repository Mandates and Policies); 24 data repositories registered with the Registry of Data Repositories (re3data.org) (although the pilot project identified 66 research data repositories); and one data repository assigned the CoreTrustSeal. Although this is a start, far more needs to be done to align African data curation and research practices with global standards. Funding to conduct research remains a challenge. African researchers mostly fund their own research, and there are little incentives for them to make their research and accompanying data sets openly accessible. Funding and peer recognition, along with an enabling research environment conducive for research, are regarded as major incentives. The landscape report concludes with a number of concerns towards sharing research data openly, as well as challenges in terms of Open Data policy, ICT infrastructure supportive of data sharing, capacity building, lack of skills, and the need for incentives. Although great progress has been made in terms of Open Science and Open Data practices, more awareness needs to be created and further advocacy efforts are required for buy-in from African governments. A federated African Open Science Platform (AOSP) will not only encourage more collaboration among researchers in addressing the SDGs, but it will also benefit the many stakeholders identified as part of the pilot phase. The time is now, for governments in Africa, to acknowledge the important role of science in general, but specifically Open Science and Open Data, through developing and aligning the relevant policies, investing in an ICT infrastructure conducive for data sharing through committing funding to making NRENs financially sustainable, incentivising open research practices by scientists, and creating opportunities for more scientists and stakeholders across all disciplines to be trained in data management.
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