Semigroups of transformations preserving an equivalence relation and a cross-section

• Autor(a) principal: Araújo, João
• Data de Publicação: 2004
• Outros Autores: Konieczny, Janusz
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.2/3806
• topic: Transformation; Equivalence relation; Idempotent; Centralizer; 20M20

For a set X, an equivalence relation ρ on X, and a cross-section R of the partition X/ρ induced by ρ, consider the semigroup T (X, ρ,R) consisting of all mappings a from X to X such that a preserves both ρ (if (x, y) ∈ ρ then (xa, ya) ∈ ρ) and R (if r ∈ R then ra ∈ R). The semigroup T (X, ρ,R) is the centralizer of the idempotent transformation with kernel ρ and image R. We determine the structure of T (X, ρ,R) in terms of Green’s relations, describe the regular elements of T (X, ρ,R), and determine the following classes of the semigroups T (X, ρ,R): regular, abundant, inverse, and completely regular.