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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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All varieties of central completely simple semigroups
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by Mario Petrich and Norman R. Reilly PDF
Trans. Amer. Math. Soc. 280 (1983), 623-636 Request permission

Abstract:

Completely simple semigroups may be considered as a variety of algebras with the binary operation of multiplication and the unary operation of inversion. A completely simple semigroup is central if the product of any two idempotents lies in the centre of the containing maximal subgroup. Central completely simple semigroups form a subvariety $\mathcal {C}$ of the variety of all completely simple semigroups. We find an isomorphic copy of $\mathcal {L}(\mathcal {C})$ as a subdirect product of the lattices $\mathcal {L}(\mathcal {R} \mathcal {B})$, $\mathcal {L}(\mathcal {A} \mathcal {G})$, and $\mathcal {L}(\mathcal {G})$ of all varieties of rectangular bands, abelian groups, and groups, respectively. We consider also several homomorphisms and study congruences they induce.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 280 (1983), 623-636
  • MSC: Primary 20M07
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0716841-1
  • MathSciNet review: 716841