Reducibility of joins involving some locally trivial pseudovarieties - Costa, José Carlos (2004)
In this paper, we show that sigma-reducibility is preserved under joins with K, where K is the pseudovariety of semigroups in which idempotents are left zeros. Reducibility of joins with D, the pseudovariety of semigroups in which idempotents are right zeros, is also considered. In this case, we were able to prove that sigma-reducibility is preserved for joins with pseudovarieties verifying a certain property of cancellation. As an example involving the semidirect product, we prove that Sl*K is k-tame, where Sl stands for the pseudovariety of semilattices.