Proper regular semigroups

Author:
F. E. Masat

Journal:
Proc. Amer. Math. Soc. **71** (1978), 189-192

MSC:
Primary 20M10

DOI:
https://doi.org/10.1090/S0002-9939-1978-0480796-1

MathSciNet review:
0480796

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1978-0480796-1

Keywords:
Proper,
group congruence,
reflexiveness,
inverse semigroups,
unitary semigroups,
orthodox semigroups

Article copyright:
© Copyright 1978
American Mathematical Society