Proper Regular Semigroups

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Sep 1978Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 71, page 189 (issn: 0002-9939,

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Authors: Masat, F. E.;

doi: 10.2307/2042830 , 10.1090/s0002-9939-1978-0480796-1

Proper Regular Semigroups

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Abstract

In a recent paper, D. B. McAlister gave several characterizations of proper inverse semigroups. In this paper, the concept of proper is extended to the class of regular semigroups. This is done by requiring that the set of idempotents of the semigroup coincides with the kernel of the minimum group congruence on the semigroup. A theorem is presented which contains several characterizations of proper regular semigroups, and the related result of McAlister then follows as a corollary. The paper concludes with some open questions and examples.

Keywords

General structure theory for semigroups

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