Relevant bibliographies by topics / Algebra

Academic literature on the topic 'Algebra'

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Published: 4 June 2021
Last updated: 31 July 2024

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Journal articles on the topic "Algebra"

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Radfar, A., and A. Rezaei. "Pseudo-BI-algebras‎: ‎Non-commutative generalization of BI-algebras." Journal of Algebraic Hyperstructures and Logical Algebras 4, no. 2 (2023): 167–87. http://dx.doi.org/10.61838/kman.jahla.4.2.11.

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We ‎define and study the pseudo BI-algebras as a generalization of BI-algebras and implication algebras and investigate some properties‎. Also‎, ‎we define distributive pseudo BI-algebras and construct a BI-algebra related to these‎. ‎Further‎, ‎we prove ‎there is no proper pseudo BI-algebra of the order less than 4 and that every pseudo BI-algebra of order 4 is a poset‎, ‎and so is a pseudo BH-algebra‎. ‎‎Beside‎, ‎we introduce exchangeable pseudo BI-algebra and show that the class of them is a proper subclass of the class pseudo CI-algebras‎. ‎Finally‎, ‎we define the notions of (weak) commutative pseudo BI-algebras and prove ‎every weak commutative pseudo BI-algebra is a (dual) pseudo BH-algebra‎, ‎but the converse is not true‎, ‎and show that every exchangeable commutative pseudo BI-algebra is an implication algebra.
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Grigoryan, S. A., and T. V. Tonev. "Blaschke inductive limits of uniform algebras." International Journal of Mathematics and Mathematical Sciences 27, no. 10 (2001): 599–620. http://dx.doi.org/10.1155/s0161171201006792.

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We consider and studyBlaschke inductive limit algebrasA(b), defined as inductive limits of disc algebrasA(D)linked by a sequenceb={Bk}k=1∞of finite Blaschke products. It is well known that bigG-disc algebrasAGover compact abelian groupsGwith ordered dualsΓ=Gˆ⊂ℚcan be expressed as Blaschke inductive limit algebras. Any Blaschke inductive limit algebraA(b)is a maximal and Dirichlet uniform algebra. Its Shilov boundary∂A(b)is a compact abelian group with dual group that is a subgroup ofℚ. It is shown that a bigG-disc algebraAGover a groupGwith ordered dualGˆ⊂ℝis a Blaschke inductive limit algebra if and only ifGˆ⊂ℚ. The local structure of the maximal ideal space and the set of one-point Gleason parts of a Blaschke inductive limit algebra differ drastically from the ones of a bigG-disc algebra. These differences are utilized to construct examples of Blaschke inductive limit algebras that are not bigG-disc algebras. A necessary and sufficient condition for a Blaschke inductive limit algebra to be isometrically isomorphic to a bigG-disc algebra is found. We consider also inductive limitsH∞(I)of algebrasH∞, linked by a sequenceI={Ik}k=1∞of inner functions, and prove a version of the corona theorem with estimates for it. The algebraH∞(I)generalizes the algebra of bounded hyper-analytic functions on an open bigG-disc, introduced previously by Tonev.
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Angeltveit, Vigleik. "Uniqueness of MoravaK-theory." Compositio Mathematica 147, no. 2 (September 27, 2010): 633–48. http://dx.doi.org/10.1112/s0010437x10005026.

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AbstractWe show that there is an essentially uniqueS-algebra structure on the MoravaK-theory spectrumK(n), whileK(n) has uncountably manyMUor$\widehat {E(n)}$-algebra structures. Here$\widehat {E(n)}$is theK(n)-localized Johnson–Wilson spectrum. To prove this we set up a spectral sequence computing the homotopy groups of the moduli space ofA∞structures on a spectrum, and use the theory ofS-algebrak-invariants for connectiveS-algebras found in the work of Dugger and Shipley [Postnikov extensions of ring spectra, Algebr. Geom. Topol.6(2006), 1785–1829 (electronic)] to show that all the uniqueness obstructions are hit by differentials.
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Kassem, M. S., and K. Rowlands. "Double multipliers andA*-algebras of the first kind." Mathematical Proceedings of the Cambridge Philosophical Society 102, no. 3 (November 1987): 507–16. http://dx.doi.org/10.1017/s0305004100067554.

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LetAbe anA*-algebra and letdenote its auxiliary norm closure. The multiplier algebras of dualA*-algebras of the first kind have been studed by Tomiuk [12], [13] and Wong[15]. In this paper we study the double multiplier algebra ofA*-algebras of the first kind. In particular, we prove that, ifAis anA*-algebra of the first kind, then the double multiplier algebraM(A) ofAis *-isomorphic and (auxiliary norm) isometric to a subalgebra ofM(), extending in the process some results established by Tomiuk[12]. We also consider the embedding of the double multiplier algebra ofAin**, when the latter is regarded as an algebra with the Arens product, and, in particular, we show that, for an annihilator A*-algebra,M(A) is *-isomorphic and (auxiliary norm) isometric to**.
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Caprau, Carmen. "Twin TQFTs and Frobenius Algebras." Journal of Mathematics 2013 (2013): 1–25. http://dx.doi.org/10.1155/2013/407068.

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We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on atwin Frobenius algebra, by providing a description of this category in terms of generators and relations. A twin Frobenius algebra(C,W,z,z∗)consists of a commutative Frobenius algebraC, a symmetric Frobenius algebraW, and an algebra homomorphismz:C→Wwith dualz∗:W→C, satisfying some extra conditions. We also introduce a generalized 2-dimensional Topological Quantum Field Theory defined on singular 2-dimensional cobordisms and show that it is equivalent to a twin Frobenius algebra in a symmetric monoidal category.
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Padhan, Rudra Narayan, and K. C. Pati. "Some studies on central derivation of nilpotent Lie superalgebra." Asian-European Journal of Mathematics 13, no. 04 (December 7, 2018): 2050068. http://dx.doi.org/10.1142/s1793557120500680.

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Many theorems and formulas of Lie superalgebras run quite parallel to Lie algebras, sometimes giving interesting results. So it is quite natural to extend the new concepts of Lie algebra immediately to Lie superalgebra case as the later type of algebras have wide applications in physics and related theories. Using the concept of isoclinism, Saeedi and Sheikh-Mohseni [A characterization of stem algebras in terms of central derivations, Algebr. Represent. Theory 20 (2017) 1143–1150; On [Formula: see text]-derivations of Filippov algebra, to appear in Asian-Eur. J. Math.; S. Sheikh-Mohseni, F. Saeedi and M. Badrkhani Asl, On special subalgebras of derivations of Lie algebras, Asian-Eur. J. Math. 8(2) (2015) 1550032] recently studied the central derivation of nilpotent Lie algebra with nilindex 2. The purpose of the present paper is to continue and extend the investigation to obtain some similar results for Lie superalgebras, as isoclinism in Lie superalgebra is being recently introduced.
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Feeman, Timothy G. "The Bourgain algebra of a nest algebra." Proceedings of the Edinburgh Mathematical Society 40, no. 1 (February 1997): 151–66. http://dx.doi.org/10.1017/s0013091500023518.

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In analogy with a construction from function theory, we herein define right, left, and two-sided Bourgain algebras associated with an operator algebra A. These algebras are defined initially in Banach space terms, using the weak-* topology on A, and our main result is to give a completely algebraic characterization of them in the case where A is a nest algebra. Specifically, if A = alg N is a nest algebra, we show that each of the Bourgain algebras defined has the form A + K ∩ B, where B is the nest algebra corresponding to a certain subnest of N. We also characterize algebraically the second-order (and higher) Bourgain algebras of a nest algebra, showing for instance that the second-order two-sided Bourgain algebra coincides with the two-sided Bourgain algebra itself in this case.
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BOKUT, L. A., YUQUN CHEN, and QIUHUI MO. "GRÖBNER–SHIRSHOV BASES AND EMBEDDINGS OF ALGEBRAS." International Journal of Algebra and Computation 20, no. 07 (November 2010): 875–900. http://dx.doi.org/10.1142/s0218196710005923.

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In this paper, by using Gröbner–Shirshov bases, we show that in the following classes, each (respectively, countably generated) algebra can be embedded into a simple (respectively, two-generated) algebra: associative differential algebras, associative Ω-algebras, associative λ-differential algebras. We show that in the following classes, each countably generated algebra over a countable field k can be embedded into a simple two-generated algebra: associative algebras, semigroups, Lie algebras, associative differential algebras, associative Ω-algebras, associative λ-differential algebras. We give another proofs of the well known theorems: each countably generated group (respectively, associative algebra, semigroup, Lie algebra) can be embedded into a two-generated group (respectively, associative algebra, semigroup, Lie algebra).
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Xin, Xiao-Long, and Pu Wang. "States and Measures on Hyper BCK-Algebras." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/397265.

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We define the notions of Bosbach states and inf-Bosbach states on a bounded hyper BCK-algebra(H,∘,0,e)and derive some basic properties of them. We construct a quotient hyper BCK-algebra via a regular congruence relation. We also define a∘-compatibledregular congruence relationθand aθ-compatibledinf-Bosbach stateson(H,∘,0,e). By inducing an inf-Bosbach states^on the quotient structureH/[0]θ, we show thatH/[0]θis a bounded commutative BCK-algebra which is categorically equivalent to an MV-algebra. In addition, we introduce the notions of hyper measures (states/measure morphisms/state morphisms) on hyper BCK-algebras, and present a relation between hyper state-morphisms and Bosbach states. Then we construct a quotient hyper BCK-algebraH/Ker(m)by a reflexive hyper BCK-idealKer(m). Further, we prove thatH/Ker(m)is a bounded commutative BCK-algebra.
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Patlertsin, Sutida, Suchada Pongprasert, and Thitarie Rungratgasame. "On Inner Derivations of Leibniz Algebras." Mathematics 12, no. 8 (April 11, 2024): 1152. http://dx.doi.org/10.3390/math12081152.

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Leibniz algebras are generalizations of Lie algebras. Similar to Lie algebras, inner derivations play a crucial role in characterizing complete Leibniz algebras. In this work, we demonstrate that the algebra of inner derivations of a Leibniz algebra can be decomposed into the sum of the algebra of left multiplications and a certain ideal. Furthermore, we show that the quotient of the algebra of derivations of the Leibniz algebra by this ideal yields a complete Lie algebra. Our results independently establish that any derivation of a semisimple Leibniz algebra can be expressed as a combination of three derivations. Additionally, we compare the properties of the algebra of inner derivations of Leibniz algebras with the algebra of central derivations.
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Dissertations / Theses on the topic "Algebra"

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Alghamdi, Mohamed A. M. A. "Some problems in algebraic topology : polynomial algebras over the Steenrod algebra." Thesis, University of Aberdeen, 1991. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=166808.

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We prove two theorems concerning the action of the Steenrod algebra in cohomology and homology. (i) Let A denote a finitely generated graded Fp polynomial algebra over the Steenrod algebra whose generators have dimensions not divisible by p. The possible sets of dimensions of the generators for such A are known. It was conjectured that if we replaced the polynomial algebra A by a polynomial algebra truncated at some height greater than p over the Steenrod algebras, the sets of all possible dimensions would coincide with the former list. We show that the conjecture is false. For example F11[x6,x10]12 truncated at height 12 supports an action of the Steenrod algebra but F11[x6,x10] does not. (ii) Let V be an elementary abelian 2-group of rank 3. The problem of determining a minimal set of generators for H*(BV,F2) over the Steenrod algebra was an unresolved problem for many years. (A solution was announced by Kameko in June 1990, but is not yet published.) A dual problem is to determine the subring M of the Pontrjagin ring H*(BV,F2). We determine this ring completely and in particular give a verification that the minimum number of generators needed in each dimension in cohomology is as announced by Kameko, but by using completely different techniques. Let v ε V - (0) and denote by a_5(v) ε H*(BV,F2) the image of the non-zero class in H2s-1(RP∞,F2) imeq F2 under the homomorphism induced by the inclusion of F2 → V onto (0,v). We show that M is isomorphic to the ring generated by (a_s(v),s ≥ 1, v ε V - (0)) except in dimensions of the form 2^r+3 + 2^r+1 + 2^r - 3, r ≥ 0, where we need to adjoin our additional generator.
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Rigby, Simon W. "Steinberg algebra and Leavitt path algebras." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29433.

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Leavitt path algebras are a new and exciting subject in noncommutative ring theory. To each directed graph E, and unital commutative ring R, is associated an R-algebra called the Leavitt path algebra of E with coefficients in R. It was discovered, when the theory of Leavitt path algebras was already quite advanced, that some of the more difficult questions were susceptible to a new approach using topological groupoids. Taking a special kind of groupoid G, one can construct an R-algebra called the Steinberg algebra of G. Many interesting classes of algebras, including Leavitt path algebras, can be obtained from this process. This dissertation is an exposition of the recent advances achieved by the groupoid approach to Leavitt path algebras. New proofs are presented to show that the boundary path groupoid (which underlies the Steinberg algebra model for Leavitt path algebras) has the necessary topological properties. A new theorem is presented, characterising strongly graded Leavitt path algebras in graphical terms. We show that the main results on the structure theory of Leavitt path algebras, including the simplicity and primitivity theorems, can be recovered using the groupoid approach. We demonstrate how these methods lead to an explicit description of the centre of a Leavitt path algebra.
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Galbucci, Elena. "Confronto tra algebre monounarie e algebra universale." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2011. http://amslaurea.unibo.it/1835/.

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Cid, Ruiz Yairon. "Blow-up algebras in Algebra, Geometry and Combinatorics." Doctoral thesis, Universitat de Barcelona, 2019. http://hdl.handle.net/10803/667768.

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The primary topic of this thesis lies at the crossroads of Commutative Algebra and its interactions with Algebraic Geometry and Combinatorics. It is mainly focused around the following themes: 1) Defining equations of blow-up algebras; 2) Study of rational maps via blow-up algebras; and 3) Asymptotic properties of the powers of edge ideals of graphs. We are primarily interested in questions that arise in geometrical or combinatorial contexts and try to understand how their possible answers manifest in various algebraic structures or invariants. There is a particular algebraic object, the Rees algebra (or blow-up algebra), that appears in many constructions of Commutative Algebra, Algebraic Geometry, Geometric Modeling, Computer Aided Geometric Design and Combinatorics. The work horse and main topic of this doctoral dissertation has been the study of this algebra under various situations. The Rees algebra was introduced in the field of Commutative Algebra in the famous paper published in 1958. Since then it has become a central and fundamental object with numerous applications. The study of this algebra has been so fruitful that it is difficult to single out particular results or papers. From a geometrical point of view, the Rees algebra corresponds with the bi-homogeneous coordinate ring of two fundamental objects: the blow-up of a projective variety along a subvariety and the graph of a rational map between projective varieties. Therefore, the importance of finding the defining equations of the Rees algebra is probably beyond argument. This is a problem of tall order that has occupied commutative algebraists and algebraic geometers, and despite an extensive effort, it remains open even in the case of polynomial rings in two variables. In Chapter 2 of this dissertation, we use the theory of D-module s to describe the defining ideal of the Rees algebra in the case of a parametrization of a plane curve. In a joint work with Buse and D'Andrea, Chapter 3 of this dissertation , we introduce a new algebra that we call the saturated special fiber ring, which turns out to be an important tool to analyze the degree of a rational map. Later, in Chapter 4 of this dissertation, we compute the multiplicity of this new algebra in the case of perfect ideals of height two, which, in particular, provides an effective method to determine the degree of a rational map having those ideals as base ideal. In a joint work with Simis, Chapte r 5 of this dissertation, we consider the behavior of the degree of a rational map under specialization of the coefficients of the defining linear system. The Rees algebra of the edge ideal of a graph is a well studied object, that relates combinatorial properties of a graph with algebraic in variants of the powers of its edge ideal. For the Rees algebra of the edge ideal of a bipartite graph, Chapter 6 of this dissertation, we compute the universal Grobner basis of its defining equations and its total Castelnuovo-Mumford regularity as a bigraded algebra. It is a celeb rated result that the regularity of the powers of a homogeneous ideal is asymptotically a linear function. Considerable efforts have been put forth to understand the form of this asymptotic linear function in the case of edge ideals. In a joint work with Jafari, Picone and Nemati, Chapter 7 of this dissertation, for bicyclic graphs, i.e. graphs containing exactly two cycles, we characterize the regularity of its edge ideal in terms of the induced matching number and determine the previous asymptotic linear function in special cases.
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Hadi, Shazia. "Applications of the Pauli algebra and other geometric algebras." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ52560.pdf.

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Banjo, Elizabeth. "Representation theory of algebras related to the partition algebra." Thesis, City University London, 2013. http://openaccess.city.ac.uk/2360/.

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The main objective of this thesis is to determine the complex generic representation theory of the Juyumaya algebra. We do this by showing that a certain specialization of this algebra is isomorphic to the small ramified partition algebra, introduced by Martin (the representation theory of which is computable by a combination of classical and category theoretic techniques). We then use this result and general arguments of Cline, Parshall and Scott to prove that the Juyumaya algebra En(x) over the complex field is generically semisimple for all n 2 N. The theoretical background which will facilitate an understanding of the construction process is developed in suitable detail. We also review a result of Martin on the representation theory of the small ramified partition algebra, and fill in some gaps in the proof of this result by providing proofs to results leading to it.
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Hmaida, Mufida Mohamed A. "Representation theory of algebras related to the bubble algebra." Thesis, University of Leeds, 2016. http://etheses.whiterose.ac.uk/15987/.

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In this thesis we study several algebras which are related to the bubble algebra, including the bubble algebra itself. We introduce a new class of multi-parameter algebras, called the multi-colour partition algebra $ P_{n,m} ( \breve{\delta} )$, which is a generalization of both the partition algebra and the bubble algebra. We also define the bubble algebra and the multi-colour symmetric groupoid algebra as sub-algebras of the algebra $ P_{n,m} ( \breve{\delta} ) $. We investigate the representation theory of the multi-colour symmetric groupoid algebra $ \F S_{n,m} $. We show that $ \F S_{n,m} $ is a cellular algebra and it is isomorphic to the generalized symmetric group algebra $ \F \mathbb{Z}_m \wr S_n $ when $ m $ is invertible and $ \F $ is an algebraically closed field. We then prove that the algebra $ P_{n,m} ( \breve{\delta} ) $ is also a cellular algebra and define its cell modules. We are therefore able to classify all the irreducible modules of the algebra $ P_{n,m} ( \breve{\delta} ) $. We also study the semi-simplicity of the algebra $ P_{n,m} ( \breve{\delta} ) $ and the restriction rules of the cell modules to lower rank $ n $ over the complex field. The main objective of this thesis is to solve some open problems in the representation theory of the bubble algebra $ T_{n,m} ( \breve{\delta} ) $. The algebra $ T_{n,m} ( \breve{\delta} ) $ is known to be cellular. We use many results on the representation theory of the Temperley-Lieb algebra to compute bases of the radicals of cell modules of the algebra $ T_{n,m} ( \breve{\delta} ) $ over an arbitrary field. We then restrict our attention to study representations of $ T_{n,m} ( \breve{\delta} ) $ over the complex field, and we determine the entire Loewy structure of cell modules of the algebra $ T_{n,m} ( \breve{\delta} ) $. In particular, the main theorem is Theorem 5.41.
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Bertram, Wolfgang. "The geometry of Jordan and Lie structures /." Berlin [u.a.] : Springer, 2000. http://www.loc.gov/catdir/enhancements/fy0816/00066150-d.html.

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Pawloski, Robert Michael. "Computing the Cohomology Ring and Ext-Algebra of Group Algebras." Diss., The University of Arizona, 2006. http://hdl.handle.net/10150/194298.

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This dissertation describes an algorithm and its implementation in the computer algebra system GAP for constructing the cohomology ring and Ext-algebra for certain group algebras kG. We compute in the Morita equivalent basic algebra B of kG and obtain the cohomology ring and Ext-algebra for the group algebra kG up to isomorphism. As this work is from a computational point of view, we consider the cohomology ring and Ext-algebra via projective resolutions.There are two main methods for computing projective resolutions. One method uses linear algebra and the other method uses noncommutative Grobner basis theory. Both methods are implemented in GAP and results in terms of timings are given. To use the noncommutative Grobner basis theory, we have implemented and designed an alternative algorithm to the Buchberger algorithm when given a finite dimensional algebra in terms of a basis consisting of monomials in the generators of the algebra and action of generators on the basis.The group algebras we are mainly concerned with here are for simple groups in characteristic dividing the order of the group. We have computed the Ext-algebra and cohomology ring for a variety of simple groups to a given degree and have thus added many more examples to the few that have thus far been computed.
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Linckelmann, Markus. "Variations sur les blocs a groupes de defaut cycliques." Paris 7, 1988. http://www.theses.fr/1988PA077209.

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Le present travail a pour but d'une part de donner une presentatgion complete des resultats connus sur les blocs a groupes de defaut cycliques, en traitant d'abord les proprietes qui ne dependent que de l'algebre du bloc en tant qu'algebre abstraite et ensuite les proprietes qui proviennent de la presence d'un groupe, et d'autre part d'exposer quelques resultats nouveaux concernant la structure de l'algebre de source et une description de l'algebre du bloc en tant que algebre commutante des suites exactes de green associes au bloc
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Books on the topic "Algebra"

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Kondrat'ev, Gennadiy. Clifford Geometric Algebra. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1832489.

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The monograph is devoted to the fundamental aspects of geometric algebra and closely related issues. The category of Clifford algebras is considered as the conjugate category of vector spaces with a quadratic form. Possible constructions in this category and internal algebraic operations of an algebra with a geometric interpretation are studied. An application to the differential geometry of a Euclidean manifold based on a shape tensor is included. We consider products, coproducts and tensor products in the category of associative algebras with application to the decomposition of Clifford algebras into simple components. Spinors are introduced. Methods of matrix representation of the Clifford algebra are studied. It may be of interest to students, postgraduates and specialists in the field of mathematics, physics and cybernetics.
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Hartfiel, D. J. Elementary linear algebra. Boston: Prindle, Weber & Schmidt, 1987.

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Andrilli, Stephen Francis. Elementary linear algebra. 3rd ed. Amsterdam: Elsevier Academic Press, 2003.

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Andrilli, Stephen Francis. Elementary linear algebra. Boston: PWS-Kent, 1993.

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Venit, Stewart. Elementary linear algebra. 3rd ed. Boston: PWS-Kent Pub. Co., 1989.

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Venit, Stewart. Elementary linear algebra. 2nd ed. Boston: Prindle, Weber & Schmidt, 1987.

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Penney, Richard C. Linear algebra: Ideas and applications. New York: J. Wiley, 1998.

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Deskins, W. E. Abstract algebra. New York: Dover Publications, 1995.

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Bosch, Siegfried. Algebraic Geometry and Commutative Algebra. London: Springer London, 2013.

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Bretscher, Otto. Linear algebra with applications. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2001.

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Book chapters on the topic "Algebra"

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Zeidler, Eberhard. "Algebras and Duality (Tensor Algebra, Grassmann Algebra, Clifford Algebra, Lie Algebra)." In Quantum Field Theory III: Gauge Theory, 115–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22421-8_3.

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Shafarevich, Igor R. "Lie Algebras and Nonassociative Algebra." In Encyclopaedia of Mathematical Sciences, 188–201. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/3-540-26474-4_19.

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Villoria, Alejandro, Henning Basold, and Alfons Laarman. "Enriching Diagrams with Algebraic Operations." In Lecture Notes in Computer Science, 121–43. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-57228-9_7.

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AbstractIn this paper, we extend diagrammatic reasoning in monoidal categories with algebraic operations and equations. We achieve this by considering monoidal categories that are enriched in the category of Eilenberg-Moore algebras for a monad. Under the condition that this monad is monoidal and there is an adjunction between the free algebra functor and the underlying category functor, we construct an adjunction between symmetric monoidal categories and symmetric monoidal categories enriched over algebras for the monad. This allows us to devise an extension, and its semantics, of the ZX-calculus with probabilistic choices by freely enriching over convex algebras, which are the algebras of the finite distribution monad. We show how this construction can be used for diagrammatic reasoning of noise in quantum systems.
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Schmid, Todd, Tobias Kappé, and Alexandra Silva. "A Complete Inference System for Skip-free Guarded Kleene Algebra with Tests." In Programming Languages and Systems, 309–36. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30044-8_12.

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AbstractGuarded Kleene Algebra with Tests (GKAT) is a fragment of Kleene Algebra with Tests (KAT) that was recently introduced to reason efficiently about imperative programs. In contrast to KAT, GKAT does not have an algebraic axiomatization, but relies on an analogue of Salomaa’s axiomatization of Kleene Algebra. In this paper, we present an algebraic axiomatization and prove two completeness results for a large fragment of GKAT consisting of skip-free programs.
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Lehmann, Günter. "Algebra." In Modell- und rekursionstheoretische Gru ndlagen psychologischer Theorienbildung, 1–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-70595-3_1.

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Basu, Saugata, Richard Pollack, and Marie-Francoise Roy. "Algebra." In Algorithms in Real Algebraic Geometry, 91–136. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05355-3_5.

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O’Regan, Gerard. "Algebra." In Texts in Computer Science, 99–116. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-44561-8_6.

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Łojasiewicz, Stanisław. "Algebra." In Introduction to Complex Analytic Geometry, 1–71. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-7617-9_1.

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Vince, John. "Algebra." In Mathematics for Computer Graphics, 11–21. London: Springer London, 2014. http://dx.doi.org/10.1007/978-1-4471-6290-2_3.

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Peren, Franz W. "Algebra." In Formelsammlung Wirtschaftsmathematik, 39–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-47850-9_4.

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Conference papers on the topic "Algebra"

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KUBO, F. "COMPATIBLE ALGEBRA STRUCTURES OF LIE ALGEBRAS." In 5th China–Japan–Korea International Ring Theory Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812818331_0020.

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Gautier, Thierry, Jean-Louis Roch, Ziad Sultan, and Bastien Vialla. "Parallel algebraic linear algebra dedicated interface." In PASCO '15: International Workshop on Parallel Symbolic Computation. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2790282.2790286.

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Freitas, Leonardo, Augusto Sampaio, and Ana Cavalcanti. "JACK: A Framework for Process Algebra Implementation in Java." In Simpósio Brasileiro de Engenharia de Software. Sociedade Brasileira de Computação, 2002. http://dx.doi.org/10.5753/sbes.2002.23941.

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The construction of concurrent programs is especially complex due mainly to the inherent non-determinism of their execution, which makes it difficult to repeat test scenarios. Process algebras have been used to design and reason about these programs. This paper presents an approach to developing concurrent programs using a set of process algebra constructs implemented as an object-oriented framework in Java, called JACK. The main objective of the framework is the design and implementation of process algebra constructs that provides as naturally as possible, the algebraic idiom as an extension package to Java. This work emphasises the use of design patterns and pattern languages to properly build frameworks like this, achieving desired software engineering properties and software quality requirements. The user of the JACK framework is able to describe its process specification in Java.
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Premkumar, M., H. Girija Bai, A. Prasanna, K. P. S. Parmar, M. S. Karuna, and Moti Lal Rinawa. "On Algebraic Characteristics of Fuzzy T-Sub algebra in T-Algebra under the Normalization." In 2022 International Conference on Computational Modelling, Simulation and Optimization (ICCMSO). IEEE, 2022. http://dx.doi.org/10.1109/iccmso58359.2022.00040.

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Smith, Larry. "An algebraic introduction to the Steenrod algebra." In School and Conference in Algebraic Topology. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.11.327.

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Bijev, G. "Semigroups and computer algebra in algebraic structures." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12): Proceedings of the 38th International Conference Applications of Mathematics in Engineering and Economics. AIP, 2012. http://dx.doi.org/10.1063/1.4766808.

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Kozhukhov, Igor Borisovich, and Ksenia Anatolievna Kolesnikova. "Some conditions of finiteness on polygons over semigroups." In Academician O.B. Lupanov 14th International Scientific Seminar "Discrete Mathematics and Its Applications". Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/dms-2022-68.

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A polygon over a semigroup is an algebraic model machine. A finiteness condition in algebra is any condition which is satisfied by all finite algebras. The following finiteness conditions in acts over semigroups: Artinianity, Noetherian, Hopfian, Kohopfian, Cantorian, Cocantorian, the relationship between them is discussed. In addition, issues are discussed preserving or not preserving these properties with respect to the take operation direct product and coproduct.
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Widodo, Nugroho Dwi, Shely Mutiara Maghfira, Rizky Rosjanuardi, and Sumanang Muhtar Gozali. "Connection between Cohn path algebra and C*-algebra through Leavitt path algebra." In INTERNATIONAL SEMINAR ON MATHEMATICS, SCIENCE, AND COMPUTER SCIENCE EDUCATION (MSCEIS) 2021. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0155436.

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Hellings, Jelle, Catherine L. Pilachowski, Dirk Van Gucht, Marc Gyssens, and Yuqing Wu. "From relation algebra to semi-join algebra." In DBPL 2017: The 16th International Symposium on Database Programming Languages. New York, NY, USA: ACM, 2017. http://dx.doi.org/10.1145/3122831.3122833.

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Kitahara, Daichi, and Isao Yamada. "Algebraic phase unwrapping with self-reciprocal polynomial algebra." In 2017 International Conference on Sampling Theory and Applications (SampTA). IEEE, 2017. http://dx.doi.org/10.1109/sampta.2017.8024443.

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Reports on the topic "Algebra"

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Feikes, David, William Walker, Natalie McGathey, and Bir Kafle. Algebra Readiness and Algebraic Structure as Foundational Ideas for Algebraic Learning. Purdue University, 2022. http://dx.doi.org/10.5703/1288284317454.

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Ritter, G. X., Joseph N. Wilson, and Jennifer L. Davidson. Image Algebra Synthesis. Fort Belvoir, VA: Defense Technical Information Center, March 1989. http://dx.doi.org/10.21236/ada207257.

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Aadithya, Karthik, Eric Keiter, and Ting Mei. Abstract Algebra Basics. Office of Scientific and Technical Information (OSTI), March 2019. http://dx.doi.org/10.2172/1761970.

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IOWA STATE UNIV AMES DEPT OF MATHEMATICS. Applications of Algebraic Logic and Universal Algebra to Computer Science. Fort Belvoir, VA: Defense Technical Information Center, June 1989. http://dx.doi.org/10.21236/ada210556.

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Goldman, Terrance J. Fundamental length from algebra. Office of Scientific and Technical Information (OSTI), October 2019. http://dx.doi.org/10.2172/1571586.

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Bardzell, Mike, Jennifer Bergner, Kathleen Shannon, Don Spickler, and Tyler Evans. PascGalois Abstract Algebra Classroom Resources. Washington, DC: The MAA Mathematical Sciences Digital Library, July 2008. http://dx.doi.org/10.4169/loci002636.

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McCune, W. Single axioms for Boolean algebra. Office of Scientific and Technical Information (OSTI), June 2000. http://dx.doi.org/10.2172/764208.

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Cook, Steve. Basic matrix algebra for economists. Bristol, UK: The Economics Network, January 2003. http://dx.doi.org/10.53593/n216a.

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Bradley, John S. Special Year on Numerical Linear Algebra. Fort Belvoir, VA: Defense Technical Information Center, September 1988. http://dx.doi.org/10.21236/ada208199.

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Wilson, Joseph N., D. C. Wilson, and G. X. Ritter. Image Algebra FORTRAN Preprocessor User's Manual. Fort Belvoir, VA: Defense Technical Information Center, March 1989. http://dx.doi.org/10.21236/ada208612.

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