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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
DOI: https://doi.org/10.1090/S0002-9947-1983-0716841-1
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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0716841-1
Keywords: Completely simple semigroups, varieties, central completely simple semigroups, fully invariant normal subgroups, free completely simple semigroups
Article copyright: © Copyright 1983 American Mathematical Society