Relevant bibliographies by topics / Fundamental semigroup

Academic literature on the topic 'Fundamental semigroup'

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Published: 4 June 2021
Last updated: 21 February 2023

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Journal articles on the topic "Fundamental semigroup"

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Easdown, David. "Biorder-preserving coextensions of fundamental semigroups." Proceedings of the Edinburgh Mathematical Society 31, no. 3 (October 1988): 463–67. http://dx.doi.org/10.1017/s0013091500037652.

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In any extension theory for semigroups one must determine the basic building blocks and then discover how they fit together to create more complicated semigroups. For example, in group theory the basic building blocks are simple groups. In semigroup theory however there are several natural choices. One that has received considerable attention, particularly since the seminal work on inverse semigroups by Munn ([14, 15]), is the notion of a fundamental semigroup. A semigroup is called fundamental if it cannot be [shrunk] homomorphically without collapsing some of its idempotents (see below for a precise definition).
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Wang, Shoufeng. "On generalized Ehresmann semigroups." Open Mathematics 15, no. 1 (September 6, 2017): 1132–47. http://dx.doi.org/10.1515/math-2017-0091.

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Abstract As a generalization of the class of inverse semigroups, the class of Ehresmann semigroups is introduced by Lawson and investigated by many authors extensively in the literature. In particular, Gomes and Gould construct a fundamental Ehresmann semigroup CE from a semilattice E which plays for Ehresmann semigroups the role that TE plays for inverse semigroups, where TE is the Munn semigroup of a semilattice E. From a varietal perspective, Ehresmann semigroups are derived from reduction of inverse semigroups. In this paper, from varietal perspective Ehresmann semigroups are extended to generalized Ehresmann semigroups derived instead from normal orthodox semigroups (i.e. regular semigroups whose idempotents form normal bands) with an inverse transversal. We present here a semigroup C(I,Λ,E∘) from an admissible triple (I, Λ, E∘) that plays for generalized Ehresmann semigroups the role that CE from a semilattice E plays for Ehresmann semigroups. More precisely, we show that a semigroup is a fundamental generalized Ehresmann semigroup whose admissible triple is isomorphic to (I, Λ, E∘) if and only if it is (2,1,1,1)-isomorphic to a quasi-full (2,1,1,1)-subalgebra of C(I,Λ,E∘). Our results generalize and enrich some results of Fountain, Gomes and Gould on weakly E-hedges semigroups and Ehresmann semigroups.
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Neeb, Karl-Hermann. "On the fundamental group of a Lie semigroup." Glasgow Mathematical Journal 34, no. 3 (September 1992): 379–94. http://dx.doi.org/10.1017/s0017089500008983.

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The simplest type of Lie semigroups are closed convex cones in finite dimensional vector spaces. In general one defines a Lie semigroup to be a closed subsemigroup of a Lie group which is generated by one-parameter semigroups. If W is a closed convex cone in a vector space V, then W is convex and therefore simply connected. A similar statement for Lie semigroups is false in general. There exist generating Lie semigroups in simply connected Lie groups which are not simply connected (Example 1.15). To find criteria for cases when this is true, one has to consider the homomorphisminduced by the inclusion mapping i:S→G, where S is a generating Lie semigroup in the Lie group G. Our main results concern the description of the image and the kernel of this mapping. We show that the image is the fundamental group of the largest covering group of G, into which S lifts, and that the kernel is the fundamental group of the inverse image of 5 in the universal covering group G. To get these results we construct a universal covering semigroup S of S. If j: H(S): = S ∩ S-1 →S is the inclusion mapping of the unit group of S into S, then it turns out that the kernel of the induced mappingmay be identfied with the fundamental group of the unit group H(S)of S and that its image corresponds to the intersection H(S)0 ⋂π1(S), where π1(s) is identified with a central subgroup of S.
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Miller, Craig, and Nik Ruškuc. "Right noetherian semigroups." International Journal of Algebra and Computation 30, no. 01 (September 25, 2019): 13–48. http://dx.doi.org/10.1142/s0218196719500632.

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A semigroup [Formula: see text] is right noetherian if every right congruence on [Formula: see text] is finitely generated. In this paper, we present some fundamental properties of right noetherian semigroups, discuss how semigroups relate to their substructures with regard to the property of being right noetherian, and investigate whether this property is preserved under various semigroup constructions.
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Urlu Özalan, Nurten, A. Sinan Çevik, and Eylem Güzel Karpuz. "A new semigroup obtained via known ones." Asian-European Journal of Mathematics 12, no. 06 (October 14, 2019): 2040008. http://dx.doi.org/10.1142/s1793557120400082.

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The goal of this paper is to establish a new class of semigroups based on both Rees matrix and completely [Formula: see text]-simple semigroups. We further present some fundamental properties and finiteness conditions for this new semigroup structure.
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Edwards, P. M. "Fundamental semigroups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 99, no. 3-4 (1985): 313–17. http://dx.doi.org/10.1017/s0308210500014323.

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SynopsisAn idempotent-separating congruence μ is studied further in this paper. It is shown to satisfy special properties with respect to regular elements and to group-bound elements. It is shown that for any semigroup S, μ is the identity congruence on S/μ. From this, it can be shown that S/μ is fundamental for any semigroup S. Some alternative characterizations of μ are given and applied to yield sufficient conditions for a subsemigroup T of S to satisfy μ (T) = μ (S) ∩ (T × T), whence T is fundamental if S is fundamental.
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Habib, Sana, Harish Garg, Yufeng Nie, and Faiz Muhammad Khan. "An Innovative Approach towards Possibility Fuzzy Soft Ordered Semigroups for Ideals and Its Application." Mathematics 7, no. 12 (December 3, 2019): 1183. http://dx.doi.org/10.3390/math7121183.

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The objective of this paper is put forward the novel concept of possibility fuzzy soft ideals and the possibility of fuzzy soft interior ideals. The various results in the form of the theorems with these notions are presented and further validated by suitable examples. In modern life decision-making problems, there is a wide applicability of the possibility fuzzy soft ordered semigroup which has also been constructed in the paper to solve the decision-making process. Elementary and fundamental concepts including regular, intra-regular and simple ordered semigroups in terms of possibility fuzzy soft ordered semigroup are presented. Later, the concept of left (resp. right) regular and left (resp. right) simple in terms of possibility fuzzy soft ordered semigroups are delivered. Finally, the notion of possibility fuzzy soft semiprime ideals in an ordered semigroup is defined and illustrated by theorems and example.
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Simard, Arnaud. "Counterexamples concerning powers of sectorial operators on a Hilbert space." Bulletin of the Australian Mathematical Society 60, no. 3 (December 1999): 459–68. http://dx.doi.org/10.1017/s0004972700036613.

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We give explicit constructions of semigroups and operators with particular properties. First we build a bounded C0-semigroup which is invertible and which is not similar to a semigroup of contractions. Afterwards we exhibit operators which admit bounded imaginary powers of angle ω > 0 on a Hilbert space but which do not admit a bounded functional calculus on the sector of angle ω. (This gives the limit of McIntosh's fundamental result.) Finally we build, in the 2-dimensional Hilbert space, an operator which is not the negative generator of a semigroup of contractions, although its imaginary powers are bounded by eπ|s|/2.
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Goberstein, Simon M. "Inverse semigroups with certain types of partial automorphism monoids." Glasgow Mathematical Journal 32, no. 2 (May 1990): 189–95. http://dx.doi.org/10.1017/s0017089500009204.

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AbstractFor an inverse semigroup S, the set of all isomorphisms betweeninverse subsemigroups of S is an inverse monoid under composition which is denoted by (S) and called the partial automorphism monoid of S. Kirkwood [7] and Libih [8] determined which groups have Clifford partial automorphism monoids. Here we investigate the structure of inverse semigroups whose partial automorphism monoids belong to certain other important classes of inverse semigroups. First of all, we describe (modulo so called “exceptional” groups) all inverse semigroups S such that (S) is completely semisimple. Secondly, for an inverse semigroup S, we find a convenient description of the greatest idempotent-separating congruence on (S), using a well-known general expression for this congruence due to Howie, and describe all those inverse semigroups whose partial automorphism monoids are fundamental.
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van Gool, Samuel J., and Benjamin Steinberg. "Merge Decompositions, Two-sided Krohn–Rhodes, and Aperiodic Pointlikes." Canadian Mathematical Bulletin 62, no. 1 (January 7, 2019): 199–208. http://dx.doi.org/10.4153/cmb-2018-014-8.

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AbstractThis paper provides short proofs of two fundamental theorems of finite semigroup theory whose previous proofs were significantly longer, namely the two-sided Krohn-Rhodes decomposition theorem and Henckell’s aperiodic pointlike theorem. We use a new algebraic technique that we call the merge decomposition. A prototypical application of this technique decomposes a semigroup $T$ into a two-sided semidirect product whose components are built from two subsemigroups $T_{1}$, $T_{2}$, which together generate $T$, and the subsemigroup generated by their setwise product $T_{1}T_{2}$. In this sense we decompose $T$ by merging the subsemigroups $T_{1}$ and $T_{2}$. More generally, our technique merges semigroup homomorphisms from free semigroups.
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Dissertations / Theses on the topic "Fundamental semigroup"

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Roberts, Brad. "On bosets and fundamental semigroups." Thesis, The University of Sydney, 2007. http://hdl.handle.net/2123/2183.

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The term boset was coined by Patrick Jordan, both as an abbreviation of biordered set, and as a generalisation of poset, itself an abbreviation of partially ordered set. A boset is a set equipped with a partial multiplication and two intertwining reflexive and transitive arrow relations which satisfy certain axioms. When the arrow relations coincide the boset becomes a poset. Bosets were invented by Nambooripad (in the 1970s) who developed his own version of the theory of fundamental regular semigroups, including the classical theory of fundamental inverse semigroups using semilattices, due to Munn (in the 1960s). A semigroup is fundamental if it cannot be shrunk homomorphically without collapsing its skeleton of idempotents, which is a boset. Nambooripad constructed the maximum fundamental regular semigroup with a given boset of idempotents. Fundamental semigroups and bosets are natural candidates for basic building blocks in semigroup theory because every semigroup is a coextension of a fundamental semigroup in which the boset of idempotents is undisturbed. Recently Jordan reproved Nambooripad's results using a new construction based on arbitrary bosets. In this thesis we prove that this construction is always fundamental, which was previously known only for regular bosets, and also that it possesses a certain maximality property with respect to semigroups which are generated by regular elements. For nonregular bosets this constuction may be regular or nonregular. We introduce a class of bosets, called sawtooth bosets, which contain many regular and nonregular examples, and correct a criterion of Jordan's for the regularity of this construction for sawtooth bosets with two teeth. We also introduce a subclass, called cyclic sawtooth bosets, also containing many regular and nonregular examples, for which the construction is always regular.
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Roberts, Brad. "On bosets and fundamental semigroups." University of Sydney, 2007. http://hdl.handle.net/2123/2183.

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Doctor of Philosphy (PhD)
The term boset was coined by Patrick Jordan, both as an abbreviation of biordered set, and as a generalisation of poset, itself an abbreviation of partially ordered set. A boset is a set equipped with a partial multiplication and two intertwining reflexive and transitive arrow relations which satisfy certain axioms. When the arrow relations coincide the boset becomes a poset. Bosets were invented by Nambooripad (in the 1970s) who developed his own version of the theory of fundamental regular semigroups, including the classical theory of fundamental inverse semigroups using semilattices, due to Munn (in the 1960s). A semigroup is fundamental if it cannot be shrunk homomorphically without collapsing its skeleton of idempotents, which is a boset. Nambooripad constructed the maximum fundamental regular semigroup with a given boset of idempotents. Fundamental semigroups and bosets are natural candidates for basic building blocks in semigroup theory because every semigroup is a coextension of a fundamental semigroup in which the boset of idempotents is undisturbed. Recently Jordan reproved Nambooripad's results using a new construction based on arbitrary bosets. In this thesis we prove that this construction is always fundamental, which was previously known only for regular bosets, and also that it possesses a certain maximality property with respect to semigroups which are generated by regular elements. For nonregular bosets this constuction may be regular or nonregular. We introduce a class of bosets, called sawtooth bosets, which contain many regular and nonregular examples, and correct a criterion of Jordan's for the regularity of this construction for sawtooth bosets with two teeth. We also introduce a subclass, called cyclic sawtooth bosets, also containing many regular and nonregular examples, for which the construction is always regular.
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Churchill, Genevieve. "Theorems of Birkhoff type in pseudovarieties and e-varieties of regular semi-groups." Thesis, 1998. https://eprints.utas.edu.au/19069/1/whole_ChurchillGenevieve1998_thesis.pdf.

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This thesis is concerned with the problem of being able to use, or generalize, Birkhoff's fundamental theorems for classes of algebras which do not form varieties - particularly in pseudovarieties and e-varieties. After giving an introduction to these areas in Chapter 1, we first look at pseudovarieties, focusing on certain generalized varieties. Let Com, Nil, and N denote the generalized varieties of all commutative, nil, and nilpotent semigroups respectively. For a class W of semigroups let L (W) and G (W) denote respectively the lattices of all varieties and generalized varieties of semigroups contained in W. Almeida has shown that the mapping L (Nil ∩ Com) U {Nil ∩ Com} — G (N ∩ Com) given by W - W ∩ N is an isomorphism, and asked whether the extension of this mapping to L (Nil) U {Nil} is also an isomorphism. In Chapter 2 we consider this question. In Section 2.2 we show that the extension is not surjective. Non-injectivity is then established in Sections 2.4 - 2.6; this involves analysing sequences of words of unbounded lengths derived from the defining identities of certain nil varieties. Results of a more general nature are also given, in Section 2.3, involving the question of when two arbitrary semigroup varieties possess the same set of nilpotent semigroups. In Chapter 3 we turn to the problem of establishing analogues of Birkhoff's theorems for e-varieties. In Section 3.1 Auinger's Birkhoff-style theory for locally inverse e-varieties is expanded, to obtain a unified theory for e-varieties of locally inverse or of E-solid semigroups - that is, for the entire lattice of e-varieties in which nonmonogenic bifree objects exist. In addition an alternative unification, based on the techniques used by Kadourek and Szendrei to describe a Birkhoffstyle theory for E-solid e-varieties, is given in Section 3.2. In Section 3.3 we show that trifree objects on at least three generators exist in an e-variety V of regular semigroups if and only if V is locally E-solid; this extends Kadourek's work on the existence of trifree objects in locally orthodox e-varieties and generalizes Yeh's result on the existence of bifree objects. In conclusion, a theory of "n-free" objects is outlined in Section 3.4, indicating how analogues of the concept of a free object can be defined for any e-variety. The results presented in Sections 2.4 - 2.6 appear in [12]. The results of Chapter 3 will appear in [13].
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Books on the topic "Fundamental semigroup"

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Fundamentals of semigroup theory. Oxford: Clarendon, 1995.

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Howie, John M. ILL - Fundamentals of semigroup theory. 2004.

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Howie, John M. Fundamentals of Semigroup Theory, London Mathematical Monographs. Oxford University Press, 1996.

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Partial differential equations and operators Fundamental solutions and semigroups Part I. Bookboon, 2013.

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Partial differential equations and operators Fundamental solutions and semigroups Part II. Bookboon.com, 2013.

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Partial differential equations and operators Fundamental solutions and semigroups Part II. Bookboon, 2013.

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Partial differential equations and operators Fundamental solutions and semigroups Part II. Bookboon, 2013.

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Partial differential equations and operators Fundamental solutions and semigroups Part II. Bookboon, 2013.

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Partial differential equations and operators Fundamental solutions and semigroups Part II. Bookboon.com, 2013.

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Partial differential equations and operators Fundamental solutions and semigroups Part I. Bookboon, 2013.

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Book chapters on the topic "Fundamental semigroup"

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Dower, Peter M., and William M. McEneaney. "A max-plus fundamental solution semigroup for a class of lossless wave equations." In 2015 Proceedings of the Conference on Control and its Applications, 400–407. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2015. http://dx.doi.org/10.1137/1.9781611974072.55.

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Hoffmann, Michael, and Richard M. Thomas. "Biautomatic Semigroups." In Fundamentals of Computation Theory, 56–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11537311_6.

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Eklund, Patrik, Javier Gutiérrez García, Ulrich Höhle, and Jari Kortelainen. "Fundamentals of Quantales." In Semigroups in Complete Lattices, 45–202. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-78948-4_2.

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Verbeure, A. "Some Applications of Semigroups." In Fundamental Aspects of Quantum Theory, 233–38. Boston, MA: Springer US, 1986. http://dx.doi.org/10.1007/978-1-4684-5221-1_26.

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Dower, Peter M., William M. McEneaney, and Huan Zhang. "Max-plus fundamental solution semigroups for optimal control problems." In 2015 Proceedings of the Conference on Control and its Applications, 368–75. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2015. http://dx.doi.org/10.1137/1.9781611974072.51.

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Rozenblat, Bella V. "On Recursively Enumerable Subsets of N and Rees Matrix Semigroups over (Z3 ; + )." In Fundamentals of Computation Theory, 408–11. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44669-9_44.

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Koppenhagen, Ulla, and Ernst W. Mayr. "The complexity of the coverability, the containment, and the equivalence problems for commutative semigroups." In Fundamentals of Computation Theory, 257–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0036189.

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Cherenack, Paul. "Fundamental Groups of Elliptic Curves Internal to Locally Ringed Spaces." In Group and Semigroup Rings, Centro de Brasileiro de Pesquisas Fisicas Rio de Janeiro and University of Rochester, 1–11. Elsevier, 1986. http://dx.doi.org/10.1016/s0304-0208(08)71508-1.

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"FUNDAMENTAL REGULAR SEMIGROUPS." In Semigroups, 276–327. Routledge, 2017. http://dx.doi.org/10.4324/9780203739938-8.

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ISEKI, KIYOSHI. "SOME FUNDAMENTAL THEOREMS ON BCK." In Words, Semigroups, and Transductions, 231–38. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810908_0018.

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Conference papers on the topic "Fundamental semigroup"

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Vijayabalaji, S., and S. Sivaramakrishnan. "Anti fuzzy M-semigroup." In INTERNATIONAL CONFERENCE ON FUNDAMENTAL AND APPLIED SCIENCES 2012: (ICFAS2012). AIP, 2012. http://dx.doi.org/10.1063/1.4757511.

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Dower, Peter M., and William M. McEneaney. "A min-plus fundamental solution semigroup for a class of approximate infinite dimensional optimal control problems." In 2020 American Control Conference (ACC). IEEE, 2020. http://dx.doi.org/10.23919/acc45564.2020.9147921.

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Dower, Peter M., and William M. McEneaney. "Max-plus fundamental solution semigroups for dual operator differential Riccati equations." In 2014 4th Australian Control Conference (AUCC). IEEE, 2014. http://dx.doi.org/10.1109/aucc.2014.7358694.

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