Results 201 to 210 of about 27,754 (248)

EMBEDDING INVERSE SEMIGROUPS IN BISIMPLE CONGRUENCE-FREE INVERSE SEMIGROUPS

The Quarterly Journal of Mathematics, 1983
The 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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Semigroups of inverse quotients

Periodica Mathematica Hungarica, 2012
The 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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On Free Inverse Semigroups

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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Compact Topological Inverse Semigroups

Semigroup Forum, 2000
A 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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Pseudo-inverses in Semigroups

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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Inverse semigroups

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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Normally Ordered Inverse Semigroups

Semigroup Forum, 1998
Let \(S\) 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, 1986
In [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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Inverse Near Permutation Semigroups

Semigroup Forum, 2004
The symbol \({\mathcal T}_N\) denotes the semigroup, under composition, of all selfmaps of a set \(X\) with \(N\) elements. The `rank' of an element \(\alpha\in{\mathcal T}_N\) is defined to be \(|X\alpha|\). A subsemigroup of \({\mathcal T}_N\) is defined to be a `near permutation semigroup' if it is generated by a group \(G\) of permutations together
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F-Inverse Semigroups

Proceedings of the London Mathematical Society, 1971
McFadden, R., O'Carroll, L.
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