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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Regular semigroups satisfying certain conditions on idempotents and ideals
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by Mario Petrich PDF
Trans. Amer. Math. Soc. 170 (1972), 245-267 Request permission

Abstract:

The structure of regular semigroups is studied (1) whose poset of idempotents is required to be a tree or to satisfy a weaker condition concerning the behavior of idempotents in different $\mathcal {D}$-classes, or (2) all of whose ideals are categorical or satisfy a variation thereof. For this purpose the notions of $D$-majorization of idempotents, where $D$ is a $\mathcal {D}$-class, $\mathcal {D}$-majorization, $\mathcal {D}$-categorical ideals, and completely semisimple semigroups without contractions are introduced and several connections among them are established. Some theorems due to G. Lallement concerning subdirect products and completely regular semigroups and certain results of the author concerning completely semisimple inverse semigroups are either improved or generalized.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 170 (1972), 245-267
  • MSC: Primary 20M10
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0304522-0
  • MathSciNet review: 0304522