Costa, J. C.Teixeira, M. L.Nogueira, Conceição2025-09-102025-09-102017-02-080218-19671793-6500http://hdl.handle.net/10400.8/14036This paper deals with the reducibility property of semidirect products of the form V∗D relatively to graph equation systems, where D denotes the pseudovariety of definite semigroups. We show that, if the pseudovariety V is reducible with respect to the canonical signature κ consisting of the multiplication and the (ω − 1)-power, then V ∗ D is also reducible with respect to κ.engPseudovarietyDefinite semigroupSemidirect productImplicit signatureGraph equationsReducibilityjournal article10.1142/s0218196717500023