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Quantum inverse semigroups [PDF]
Journal of Noncommutative Geometry, 2022 In this work, the notion of a quantum inverse semigroup is introduced as a linearized generalization of inverse semigroups. Beyond the algebra of an inverse semigroup, which is the natural example of a quantum inverse semigroup, several other examples of
M. M. Alves +2 more
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Homogeneity of inverse semigroups [PDF]
International Journal of Algebra and Computation, 2017 An inverse semigroup [Formula: see text] is a semigroup in which every element has a unique inverse in the sense of semigroup theory, that is, if [Formula: see text] then there exists a unique [Formula: see text] such that [Formula: see text] and ...
Thomas Quinn-Gregson
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Expansions of Inverse Semigroups [PDF]
Journal of the Australian Mathematical Society, 2006 AbstractWe construct the freest idempotent-pure expansion of an inverse semigroup, generalizing an expansion of Margolis and Meakin for the group case. We also generalize the Birget-Rhodes prefix expansion to inverse semigroups with an application to partial actions of inverse semigroups.
Mark Verus Lawson +2 more
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Semimodularity in Congruence Lattices of Graph Inverse Semigroups
Communications in Algebra, 2021 Congruences on a graph inverse semigroup were recently described in terms of the underline graph. Based on such descriptions, we show that the congruence lattice of a graph inverse semigroup is upper semimodular but not lower semimodular.
Yongle Luo, Zheng-Pan Wang
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Graphs and their associated inverse semigroups [PDF]
Discrete Mathematics, 2015 Directed graphs have long been used to gain understanding of the structure of semigroups, and recently the structure of directed graph semigroups has been investigated resulting in a characterization theorem and an analog of Fruct's Theorem.
Tien Chih, Demitri Plessas
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On locally compact semitopological O-bisimple inverse ω-semigroups [PDF]
Topological Algebra and its Applications, 2018 We describe the structure of Hausdorff locally compact semitopological O-bisimple inverse ω- semigroups with compact maximal subgroups. In particular, we show that a Hausdorff locally compact semitopological O-bisimple inverse ω-semigroup with a compact ...
Gutik Oleg
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Finite coverings of semigroups and related structures [PDF]
International Journal of Group Theory, 2023 For a semigroup $S$, the covering number of $S$ with respect to semigroups, $\sigma_s(S)$, is the minimum number of proper subsemigroups of $S$ whose union is $S$.
Casey Donoven, Luise-Charlotte Kappe
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Approximation properties of Fell bundles over inverse semigroups and non-Hausdorff groupoids [PDF]
Advances in Mathematics, 2023 In this paper we study the nuclearity and weak containment property of reduced cross-sectional C*-algebras of Fell bundles over inverse semigroups. In order to develop the theory, we first prove an analogue of Fell's absorption trick in the context of ...
Alcides Buss, Diego Mart'inez
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Semiring and involution identities of powers of inverse semigroups [PDF]
Communications in Algebra, 2023 The set of all subsets of any inverse semigroup forms an involution semiring under set-theoretical union and element-wise multiplication and inversion.
I. Dolinka +2 more
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Semiring identities of finite inverse semigroups [PDF]
Semigroup Forum, 2022 We study the Finite Basis Problem for finite additively idempotent semirings whose multiplicative reducts are inverse semigroups. In particular, we show that each additively idempotent semiring whose multiplicative reduct is a nontrivial rook monoid ...
S. V. Gusev, Mikhail Volkov
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