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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