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Fiat categorification of the symmetric inverse semigroup $$\textit{IS}_n$$ IS n and the semigroup $$F^*_n$$ F n ∗ [PDF]
Semigroup Forum, 2017 Starting from the symmetric group Sn, we construct two fiat 2-categories. One of them can be viewed as the fiat “extension” of the natural 2-category associated with the symmetric inverse semigroup (considered as an ordered semigroup with respect to the ...
Volodymyr Mazorchuk, Paul Martin
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Semigroups of inverse quotients
Periodica Mathematica Hungarica, 2012The paper discusses the notion of left I-quotients in inverse semigroups. A subsemigroup \(S\) of an inverse semigroup \(Q\) is called a left I-order in \(Q\) (and \(Q\) is a semigroup of left I-quotients of \(S\)) if every \(q\in Q\) can be written as \(q=a^{-1}b\) where \(a,b\in S\).
Nassraddin Ghroda, Victoria Gould
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On Finite Semigroups Embeddable in Inverse Semigroups
Semigroup Forum, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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SemiGroup Forum, 2000
For a given set \(X\), denote by \(G_X\) the set of finite directed trees whose edges are labelled by members of \(X\), with two distinguished vertices. In this note, using techniques of rewriting theory, a new proof is given of the theorem of Munn that the free inverse semigroup on \(X\) is isomorphic to a semigroup defined on the set of so-called ...
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For a given set \(X\), denote by \(G_X\) the set of finite directed trees whose edges are labelled by members of \(X\), with two distinguished vertices. In this note, using techniques of rewriting theory, a new proof is given of the theorem of Munn that the free inverse semigroup on \(X\) is isomorphic to a semigroup defined on the set of so-called ...
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Mathematical Proceedings of the Cambridge Philosophical Society, 1961
Drazin (2) has recently introduced the concept of a pseudo-invertible element of an associative ring or semigroup. In this note we first show that such an element of a semigroup S may be characterized by the fact that some power of it lies in a subgroup of S.
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Drazin (2) has recently introduced the concept of a pseudo-invertible element of an associative ring or semigroup. In this note we first show that such an element of a semigroup S may be characterized by the fact that some power of it lies in a subgroup of S.
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On equations in inverse semigroups
Algebra Universalis, 2002It is shown for an inverse semigroup \(\mathcal S\) which is not a group, the system \(x_1=x_2\) and \(x_3=x_4\) of equations in \(\mathcal S\) is not equivalent to any equation as well as the disjunction \(x_1=x_2\) or \(x_3=x_4\).
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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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REPRESENTATIONS OF LOCALLY INVERSE *-SEMIGROUPS
International Journal of Algebra and Computation, 1996The first author obtained a generalization of Preston-Vagner Representation Theorem for generalized inverse *-semigroups. In this paper, we shall generalize their results for locally inverse *-semigroups. Firstly, by introducing a concept of a π-set (which is slightly different from the one in [7]), we shall construct the π-symmetric locally inverse *
Teruo Imaoka +2 more
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THE HOMOTOPY THEORY OF INVERSE SEMIGROUPS
International Journal of Algebra and Computation, 2002We show that abstract homotopy theory can be used to define a suitable notion of homotopy equivalence for inverse semigroups. As an application of our theory, we prove a theorem for inverse semigroup homomorphisms which is the exact counterpart of the well-known result in topology which states that every continuous function can be factorized into a ...
Mark V. Lawson +2 more
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The Universal Covering of an Inverse Semigroup
Applied Categorical Structures, 2008Considerable part of the article is devoted to presheaves on a small category. For example, transition injective presheaves (that is, its transition maps are injective) as well as transition bijective presheaves on a small category are described. The results obtained are applied to the category \(L(T)\), \(T\) an inverse semigroup, whose objects are ...
Jonathon Funk, Benjamin Steinberg
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