On finitely based pseudovarieties of the forms V [formula omitted] D and V [formula omitted] D[formula omitted

Abstract

Let D n be the pseudovariety of all finite semigroups in which products of length n are right zeros and let D = ⋃ n≥1 D n . It is shown in this paper that, if V is a pseudovariety of semigroups whose global g V is finitely based, then V ∗ D n ( n≥1) and V ∗ D are also finitely based. Moreover, if V is itself finitely based and contains the aperiodic five-element Brandt semigroup, then g V is also finitely based. As a further application, it is proved that the finite basis properties for g V , V ∗ D and V ∗ D n ( n≥1) are all equivalent for an arbitrary non-group monoidal pseudovariety V .