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Transactions of the American Mathematical Society

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



All varieties of central completely simple semigroups

Authors: Mario Petrich and Norman R. Reilly
Journal: Trans. Amer. Math. Soc. 280 (1983), 623-636
MSC: Primary 20M07
MathSciNet review: 716841
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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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Keywords: Completely simple semigroups, varieties, central completely simple semigroups, fully invariant normal subgroups, free completely simple semigroups
Article copyright: © Copyright 1983 American Mathematical Society