Resumen de Tameness of Pseudovariety Joins Involving \sf R

Jorge Almeida , José Carlos Costa, Marc Zeitoun

• In this paper, we establish several decidability results for pseudovariety joins of the form , where is a subpseudovariety of or the pseudovariety . Here, (resp. ) denotes the pseudovariety of all -trivial (resp. -trivial) semigroups. In particular, we show that the pseudovariety is (completely) ?-tame when is a subpseudovariety of with decidable ?-word problem and is (completely) ?-tame. Moreover, if is a ?-tame pseudovariety which satisfies the pseudoidentity x1 ? xry?+1zt? = x1 ? xryzt?, then we prove that is also ?-tame. In particular the joins , , , and are decidable.