Completely simple semigroup with basis property

Aljouiee A., Al Khalaf A.
Published 2013-10-09

Abstract

An inverse semigroup (group) S is called an inverse semigroup (group) with basis property, if each two minimal (irreducible) generating sets (with respect to inclusion) of an arbitrary subsemigroup (group) H of S is equivalent (i.e. they have the same cardinality).

It is proved that every completely simple semigroup with basis property is either group with basis property or its sandwich matrix has at most two rows or two column and its maximal subgroup is either trivial group or a primary cyclic group.
Full Text: PDF

How to Cite this Article

Aljouiee A., Al Khalaf A., Completely simple semigroup with basis property, J. Semigroup Theory Appl., 2013 (2013), Article ID 10

Copyright © 2013 Aljouiee A., Al Khalaf A.. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.