Suchergebnisse

We give new characterisations of regular Mal'tsev categories with distributive lattice of equivalence relations through variations of the so-called Triangular Lemma and Trapezoid Lemma in universal algebra. We then give new characterisations of equivalence distributive Goursat categories (which extend 3-permutable varieties) through variations of the Triangular and Trapezoid Lemmas involving reflexive and positive relations. (C) 2020 Elsevier B.V. All rights reserved. ; Centre for Mathematics of the University of Coimbra - Portuguese Government through FCT/MCTES [UIDB/00324/2020] ; Fonds de la Recherche Scientifique -FNRS Credit Sejour a l'etranger [2020/V 3/5/036 - 35714631 - JG/MF - 6977] ; info:eu-repo/semantics/publishedVersion

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. ; South African National Research FoundationNational Research Foundation - South Africa ; Centre for Mathematics of the University of Coimbra - Portuguese Government through FCT/MEC [UID/MAT/00324/2019] ; European Regional Development Fund through the Partnership Agreement PT2020 ; info:eu-repo/semantics/publishedVersion