On difunctionality of class relations

• Autor(a) principal: Hoefnagel, Michael
• Data de Publicação: 2020
• Outros Autores: Janelidze, Zurab, Rodelo, Diana
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.1/16538
• topic: Class relations; Congruence permutability; Congruence distributivity; Congruence modularity; Directly decomposable congruence classes; Difunctionality; Egg-box property; Mal'tsev condition; Mal'tsev variety; Shifting lemma; Mathematics

For a given variety V of algebras, we define a class relation to be a binary relation R subset of S(2)which is of the form R = S-2 boolean AND K for some congruence class K on A(2), where A is an algebra in V such that S subset of A. In this paper we study the following property of V : every reflexive class relation is an equivalence relation. In particular, we obtain equivalent characterizations of this property analogous to well-known equivalent characterizations of congruence-permutable varieties. This property determines a Mal'tsev condition on the variety and in a suitable sense, it is a join of Chajda's egg-box property as well as Duda's direct decomposability of congruence classes.