Pointlike reducibility of pseudovarieties of the form V ∗D

Costa, José Carlos; Nogueira, Conceição; Teixeira, Maria Lurdes

http://hdl.handle.net/10400.8/13674

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Authors

Costa, José Carlos

Nogueira, Conceição

Teixeira, Maria Lurdes

Abstract(s)

In this paper, we investigate the reducibility property of semidirect products of the form [Formula: see text] relatively to (pointlike) systems of equations of the form [Formula: see text], where [Formula: see text] d̃enotes the pseudovariety of definite semigroups. We establish a connection between pointlike reducibility of [Formula: see text] and the pointlike reducibility of the pseudovariety [Formula: see text]. In particular, for the canonical signature [Formula: see text] consisting of the multiplication and the [Formula: see text]-power, we show that [Formula: see text] is pointlike [Formula: see text]-reducible when [Formula: see text] is pointlike [Formula: see text]-reducible.