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Inverse semigroup shifts over countable alphabets
, 2015In this work we characterize shift spaces over infinite countable alphabets that can be endowed with an inverse semigroup operation. We give sufficient conditions under which zero-dimensional inverse semigroups can be recoded as shift spaces whose ...
D. Gonçalves +2 more
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The structure of a graph inverse semigroup
, 2014Given any directed graph E one can construct a graph inverse semigroupG(E), where, roughly speaking, elements correspond to paths in the graph. In this paper we study the semigroup-theoretic structure of G(E).
Z. Mesyan, James D. Mitchell
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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 \(a,b\in S\).
Ghroda, Nassraddin, Gould, Victoria
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The classifying space of an inverse semigroup
Periodica Mathematica Hungarica, 2012We refine Funk’s description of the classifying space of an inverse semigroup by replacing his $$*$$∗-semigroups by right generalized inverse $$*$$∗-semigroups.
G. Kudryavtseva, M. Lawson
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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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Compact Topological Inverse Semigroups
Semigroup Forum, 2000A topological inverse semigroup is a Hausdorff topological space together with a continuous multiplication and an inversion. With every topological inverse semigroup \(S\) one can associate its band of idempotents \(E(S)\). This paper studies compact topological inverse semigroups by relating them to their band of idempotents. Next, we describe briefly
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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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1995
Abstract In planning the chapter on inverse semigroups the main problem has been one of selection. As long ago as 1961, Clifford and Preston offered the opinion that inverse semigroups were the most promising class of semigroups for future study, and the intervening years have amply justified their forecast.
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Abstract In planning the chapter on inverse semigroups the main problem has been one of selection. As long ago as 1961, Clifford and Preston offered the opinion that inverse semigroups were the most promising class of semigroups for future study, and the intervening years have amply justified their forecast.
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Normally Ordered Inverse Semigroups
Semigroup Forum, 1998Let \(S\) be an inverse semigroup and \(E\) the set of its idempotents. Suppose that there exists a partial order \(\ll\) on \(E\) such that two idempotents are \(\ll\)-comparable if and only if they belong to the same \(\mathcal J\)-class of \(S\) and, for all \(s\in S\) and \(e,f\in Ess^{-1}\), \(e\ll f\) implies \(s^{-1}es\ll s^{-1}fs\).
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RELATIVELY FREE INVERSE SEMIGROUPS
The Quarterly Journal of Mathematics, 1986In [Trans. Am. Math. Soc. 294, 243--262 (1986; Zbl 0602.20052)] \textit{N. R. Reilly} and the author studied the semigroups in the title, with respect to such properties as being E-unitary, fundamental, combinatorial and completely semisimple. This paper continues that study. Let \(\mathcal V\) be a variety of inverse semigroups: then \(F\mathcal V_X\)
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