The finite basis problem in the pseudovariety joins of aperiodic semigroups with groups
Suppose that we take any pseudovariety of finite aperiodic semigroups which includes all finite \(\mathcal J\)-trivial semigroups, and form its join with any non-abelian group pseudovariety. The authors show that the resulting pseudovariety is not finitely based. Using a result of \textit{A. de Azevedo} [Lattices, semigroups and universal algebra, Proc. Int. Conf., Lisbon/Port. 1988, 1-11 (1990; Zbl 0728.08012)], they deduce that the join of a group pseudovariety with the pseudovariety of all finite \(\mathcal J\)-trivial semigroups is finitely based if and only if all the members of the group pseudovariety are abelian. Their methods also shed light on the finite basis problem for the joins of certain semigroup varieties and group varieties.
pseudovariety of finite aperiodic semigroups
finite \(\mathcal J\)-trivial semigroups
scientific article; zbMATH DE number 836810