Tameness of joins involving the pseudovariety of local semilattices

• Autor(es): Costa, José Carlos Cruz da ; Nogueira, Conceição
• Data: 2012
• Identificador Persistente: http://hdl.handle.net/1822/21117
• Origem: RepositóriUM - Universidade do Minho
• Assunto(s): Semigroup; Local semillatice; Tame pseudovariety; Join of pseudovarieties; Pseudoword; Graph equation system
• Tipo de Documento: Artigo
• Idioma: Inglês

Descrição

In this paper we prove that, if V is a kappa-tame pseudovariety which satisfies the pseudoidentity xy^{\omega+1}z=xyz, then the pseudovariety join LSl v V is also kappa-tame. Here, LSl denotes the pseudovariety of local semilattices and kappa denotes the implicit signature consisting of the multiplication and the (omega-1)-power. As a consequence, we deduce that LSl v V is decidable. In particular the joins LSl v Ab, LSl v G, LSl v OCR and LSl v CR are decidable.