On difunctionality of class relations

Hoefnagel, Michael; Janelidze, Zurab; Rodelo, Diana

http://hdl.handle.net/10400.1/16538

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Authors

Hoefnagel, Michael

Janelidze, Zurab

Rodelo, Diana

Abstract(s)

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.

Keywords

Class relations Congruence permutability Congruence distributivity Congruence modularity Directly decomposable congruence classes Difunctionality Egg-box property Mal'tsev condition Mal'tsev variety Shifting lemma