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Bruck–Reilly extensions of direct products of monoids and completely (0-)simple semigroups

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Abstract

We say that a class of monoids satisfies the property ℘ if every monoid in that class that admits a finitely presented Bruck–Reilly extension is finitely generated. We show that completely (0-)simple semigroups satisfy ℘, and that the direct product of two monoids in a class that satisfy ℘ also satisfies ℘ subject to a certain condition on the endomorphisms of the direct product. As a consequence of this result we obtain a new class of bands and a new class of completely regular semigroups that satisfy property ℘.

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Authors and Affiliations

  1. Centro de Álgebra da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003, Lisboa, Portugal

    Catarina A. Carvalho

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  1. Catarina A. Carvalho
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Correspondence to Catarina A. Carvalho.

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Communicated by Francis J. Pastijn.

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Carvalho, C.A. Bruck–Reilly extensions of direct products of monoids and completely (0-)simple semigroups. Semigroup Forum 79, 145–158 (2009). https://doi.org/10.1007/s00233-009-9162-0

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  • DOI: https://doi.org/10.1007/s00233-009-9162-0

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