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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Proper regular semigroups

Author: F. E. Masat
Journal: Proc. Amer. Math. Soc. 71 (1978), 189-192
MSC: Primary 20M10
MathSciNet review: 0480796
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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.

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Keywords: Proper, group congruence, reflexiveness, inverse semigroups, unitary semigroups, orthodox semigroups
Article copyright: © Copyright 1978 American Mathematical Society