Costa, José CarlosNogueira, Conceição2025-11-182025-11-182012-11Costa, J. C. and Nogueira, C., “Tameness of joins involving the pseudovariety of local semilattices”, International Journal of Algebra and Computation 7 (2012) 1250060 (35 pages).0218-19671793-6500http://hdl.handle.net/10400.8/14656In this paper we prove that, if V is a κ-tame pseudovariety which satisfies the pseudoidentity xy<jats:sup>ω+1</jats:sup>z = xyz, then the pseudovariety join LSl ∨ V is also κ-tame. Here, LSl denotes the pseudovariety of local semilattices and κ denotes the implicit signature consisting of the multiplication and the (ω – 1)-power. As a consequence, we deduce that LSl ∨ V is decidable. In particular the joins LSl ∨ Ab, LSl ∨ G, LSl ∨ OCR and LSl ∨ CR are decidable.engSemigroupLocal semillaticeTame pseudovarietyJoin of pseudovarietiesPseudowordGraph equation systemjournal article10.1142/s0218196712500609