Pointlike reducibility of pseudovarieties of the form V*D

In this paper, we investigate the reducibility property of semidirect products of the form V *D relatively to (pointlike) systems of equations of the form x1 =...= xn, where D denotes the pseudovariety of definite semigroups. We establish a connection between pointlike reducibility of V*D and the pointlike reducibility of the pseudovariety V. In particular, for the canonical signature consisting of the multiplication and the (omega-1)-power, we show that V*D is pointlike-reducible when V is pointlike-reducible.

European Regional Development Fund, through the programme COMPETE

This work was supported by the European Regional Development Fund, through the programme COMPETE, and by the Portuguese Government through FCT – Funda¸c˜ao para a Ciˆencia e a Tecnologia, under the project PEst-C/MAT/UI0013/2014.