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Equations on the semidirect product of a finite semilattice by a finite commutative monoid. (English) Zbl 0816.20052
The classes of semigroups studied in this paper are uniformly periodic pseudovarieties of finite commutative monoids. The authors consider the pseudovarieties obtained as semidirect products of each such class with the pseudovariety of all finite semilattices. The resulting product pseudovarieties are characterized in terms of the syntactic monoids which belong to them. Finally the authors obtain a defining set of identities for each such product pseudovariety.

MSC:
20M07 Varieties and pseudovarieties of semigroups
20M05 Free semigroups, generators and relations, word problems
08C15 Quasivarieties
20M14 Commutative semigroups
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