On finitely based pseudovarieties of the forms V*D and V*D_n

Abstract

Let D_n be the pseudovariety of all finite semigroups in which products of length n are right zeros and let D be the union of all D_n. It is shown in this paper that, if V is a pseudovariety of semigroups whose global gV is finitely based, then V*D_n and V*D are also finitely based. Moreover, if V is itself finitely based and contains the aperiodic five-element Brandt semigroup, then gV is also finitely based. As a further application, it is proved that the finite basis properties for gV, V*D and V*D_n are all equivalent for an arbitrary non-group monoidal pseudovariety V.