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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Proper regular semigroups
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by F. E. Masat PDF
Proc. Amer. Math. Soc. 71 (1978), 189-192 Request permission

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
  • © Copyright 1978 American Mathematical Society
  • 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