Free profinite R-trivial, locally idempotent and locally commutative semigroups

• Autor(a) principal: Costa, José Carlos
• Data de Publicação: 1999
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/36672
• topic: R-trivial semigroup; Locally idempotent and commutative; Implicit operation; Pseudovariety; Ciências Naturais::Matemáticas; Ciências Naturais::Ciências da Computação e da Informação; Science & Technology

This paper is concerned with the structure of implicit operations on R intersection with LJ1, the pseudovariety of all R-trivial, locally idempotent and locally commutative semigroups. We give a unique factorization statement, in terms of component projections and idempotent elements, for the implicit operations on R intersection with LJ1. As an application we give a combinatorial description of the languages that are both R-trivial and locally testable. A similar study is conducted for the pseudovariety DA intersection with LJ1 of locally idempotent and locally commutative semigroups in which each regular D-class is a rectangular band.