The semidirectly closed pseudovariety generated by aperiodic Brandt semigroups

• Autor(a) principal: Teixeira, M. L.
• Data de Publicação: 2001
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: https://hdl.handle.net/1822/2146
• topic: Semigroup; Semigrupoid; Graph; Pseudovariety; Implicit operation; Pseudoidentity; Decidability; Semidirect product; Semidirectly closed; Algorithm; Science & Technology

This paper presents a study of the semidirectly closed pseudovariety generated by the aperiodic Brandt semigroup $B_2$, denoted $\mathbf V^*(B_2)$. We construct a basis of pseudoidentities for the semidirect powers of the pseudovariety generated by $B_2$ which leads to the main result, which states that $\mathbf V^*(B_2)$ is decidable. Independently, using some suggestions given by J.~Almeida in his book ``Finite Semigroups and Universal Algebra", we constructed an algorithm to solve the membership problem in $\mathbf V^*(B_2)$.