THE GLOBALS OF SOME SUBPSEUDOVARIETIES OF $\mathsf{DA}$

Abstract

Let [Formula: see text] be the pseudovariety of all finite monoids whose principal right ideals have a unique generator, let [Formula: see text] be its dual, and let [Formula: see text]. Using the word problem for free pro-[Formula: see text] monoids, it is shown that the bilateral semidirect product [Formula: see text] is local, where [Formula: see text] denotes the pseudovariety of all finite semilattices. The global of the pseudovariety where [Formula: see text] is also computed and it is shown that this join is not local.