Embedding locally inverse semigroups into Rees matrix semigroups

We give a necessary and sufficient condition for a locally inverse semigroup to be embeddable into a Rees matrix semigroup over a generalized inverse semigroup.     

Tight inverse semigroups that are not bisimple

A semigroup is tight if each of its congruences is uniquely determined by each of the congruence classes. Bisimple inverse semigroups are tight, and tight semigroups are either simple or congruence-free with zero. Although congruence-free semigroups are tight, they are not necessarily bisimple. We construct tight inverse semigroups and tight inverse monoids that are neither bisimple nor congruence-free.     

A combinatorial approach to the structure of locally inverse semigroups

Semigroup Forum - We provide a simple and short proof of a multidimensional Borg-Levinson type theorem. Precisely, we prove that the knowledge of spectral boundary data determine uniquely the...     

Bisimple inverse semigroups whose idempotents are an interval

Bisimple locally compact topological inverse semigroups whose maximal subgroups are compact and whose set of idempotents is a real interval are studied in this paper. The structure of such semigroups is shown to be entirely determined by their maximal subgroups in case the semigroups come from a certain subclass which includes the connected ones. The factor semigroups moduloH are completely determined.     

Embedding inverse semigroups in coset semigroups

The setK(G) of all cosets X of a group G, modulo all subgroups of G, forms an inverse semigroup under the multiplication X*Y=smallest coset that constains XY. In this note we show that each inverse semigroup S can be embedded in some coset semigroupK(G). This follows from a result which shows that symmetric inverse semigroups can be embedded in the coset semigroups of suitable symmetric groups. We also give necessary and sufficient conditions on an inverse semigroup S in order that it should be isomorphic to someK(G). This research was supported by a grant from the National Science Foundation.     

Free inverse semigroups

This note announces a characterization of the free inverse semigroup I on a non-empty set X.     

On graph inverse semigroups

Semigroup Forum - We study the relationship between the graph inverse semigroups of two graphs when there is a directed immersion between the graphs and we provide structural information about...     

Coverages on inverse semigroups

Semigroup Forum - First we give a definition of a coverage on an inverse semigroup that is weaker than the one given by Lawson and Lenz and that generalizes the definition of a coverage on a...