Tameness of joins involving the pseudovariety of local semilattices

• Author(s): Costa, José Carlos Cruz da ; Nogueira, Conceição
• Date: 2012
• Persistent ID: http://hdl.handle.net/1822/21117
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Semigroup; Local semillatice; Tame pseudovariety; Join of pseudovarieties; Pseudoword; Graph equation system
• Document Type: Article
• Language: English

Description

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.