Tameness of pseudovariety joins involving R

• Author(s): Almeida, Jorge ; Costa, José Carlos Cruz da ; Zeitoun, Marc
• Date: 2005
• Persistent ID: http://hdl.handle.net/1822/3351
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Semigroup; Tame pseudovariety; Join of pseudovarieties; Systems of equations; Rational constraints; Implicit operation
• Document Type: Article
• Language: English

Description

2000 Mathematics Subject Classification: 20M07 (primary); 20M05, 20M35, 68Q70 (secondary). In this paper, we establish several decidability results for pseudovariety joins of the form VvW, where V is a subpseudovariety of J or the pseudovariety R. Here, J (resp. R) denotes the pseudovariety of all J-trivial (resp. R-trivial) semigroups. In particular, we show that the pseudovariety VvW is (completely) kappa-tame when V is a subpseudovariety of J with decidable kappa-word problem and W is (completely) kappa-tame. Moreover, if W is a kappa-tame pseudovariety which satisfies the pseudoidentity x_1...x_ry^{\omega+1}zt^\omega = x_1... x_ryzt^\omega, then we prove that RvW is also kappa-tame. In particular the joins RvAb, RvG, RvOCR, and RvCR are decidable.