Completely simple semigroup with basis property

Aljouiee A., Al Khalaf A.


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.

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Published: 2013-10-09

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.

Journal of Semigroup Theory and Applications

ISSN 2051-2937

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