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Title: On difunctionality of class relations
Authors: Hoefnagel, Michael
Janelidze, Zurab 
Rodelo, Diana 
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.
Issue Date: 2020
Publisher: Springer Verlag
Project: CMUC-UID/MAT/00324/2019 
Serial title, monograph or event: Algebra Universalis
Volume: 81
Issue: 19
Abstract: 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.
DOI: 10.1007/s00012-020-00651-z
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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