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On difunctionality of class relations

Author(s): Hoefnagel, Michael ; Janelidze, Zurab ; Rodelo, Diana

Date: 2020

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

Origin: Sapientia - Universidade do Algarve

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

Description

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.

Document Type Journal article
Language English
Contributor(s) Sapientia
CC Licence

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On difunctionality of class relations

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On difunctionality of class relations