Regular proper *-embedding of proper *-semigroups and rings

Adel A. Abdelkarim

Abstract


In this paper, it is shown that a cancellative semigroup is embeddable in an inverse semigroup. It is shown that finite proper *-semigroup is regular and any finite commutative proper *-semigroup is a union of groups. Also it is shown that a finite cyclic proper * semigroup is a group while an infinite one is *-embedded in a proper*-group, and any finite maximal proper*- semigroup has a proper *-extension ring. It is shown that there is a nonregular proper *-ring that cannot be *-embedded in any regular proper *-ring. Also it is shown that an Artinian proper *-ring is a finite direct product of matrix rings over skew fields. It is shown that a commutative proper * and cancellative semigroup is *-embeddable in a regular proper *-semigroup.


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Published: 2013-06-09

How to Cite this Article:

Adel A. Abdelkarim, Regular proper *-embedding of proper *-semigroups and rings, J. Semigroup Theory Appl., 2013 (2013), Article ID 2

Copyright © 2013 Adel A. Abdelkarim. 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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