Author(s): Hoefnagel, Michael ; Janelidze, Zurab ; Rodelo, Diana
Date: 2020
Persistent ID: https://hdl.handle.net/10316/89450
Origin: Estudo Geral - Universidade de Coimbra
Subject(s): Class relations, Congruence permutability, Congruence distributivity, Congruence modularity, Directly decomposable congruence classes, Difunctionality, Egg-box property, Mal’tsev condition, Mal’tsev variety, Shifting lemma.
For a given variety V of algebras, we define a class relation to be a binary relation R ⊆ S^2 which is of the form R = S^2 ∩ K for some congruence class K on A^2, where A is an algebra in V such that S ⊆ 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.
