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Semiring identities of finite inverse semigroups
Semigroup Forum, 2022We 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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On a class of inverse semigroups related to Leavitt path algebras
, 2021We introduce a class of inverse semigroups built from directed graphs that we refer to as Leavitt inverse semigroups. These semigroups are closely related to graph inverse semigroups and Leavitt path algebras.
J. Meakin, David Milan, Zhengpan Wang
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Tight and Cover-to-Join Representations of Semilattices and Inverse Semigroups
Operator Theory, Functional Analysis and Applications, 2019We discuss the relationship between tight and cover-to-join representations of semilattices and inverse semigroups, showing that a slight extension of the former, together with an appropriate selection of codomains, makes the two notions equivalent. As a
R. Exel
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Partial actions and an embedding theorem for inverse semigroups
Periodica Mathematica Hungarica, 2017We give a simple construction involving partial actions which permits us to obtain an easy proof of a weakened version of L. O’Carroll’s theorem on idempotent pure extensions of inverse semigroups.
M. Khrypchenko
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EMBEDDING INVERSE SEMIGROUPS IN BISIMPLE CONGRUENCE-FREE INVERSE SEMIGROUPS
The Quarterly Journal of Mathematics, 1983The authors prove that for every infinite cardinal m there exists a bisimple congruence-free inverse semigroup \(S_ m\) with \(| S_ m| =2^ m\) such that every inverse semigroup of cardinal not exceeding m can be embedded in \(S_ m\). They also show that if S is an inverse semigroup and if \(m=| S|\) if \(| S|\) is infinite and \(m=\aleph_ 0\) otherwise,
Leemans, H., Pastijn, F.
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