On difunctionality of class relations
| Autor: | Diana Rodelo, Michael Hoefnagel, Zurab Janelidze |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mal'tsev condition
Class (set theory) Property (philosophy) 0102 computer and information sciences 01 natural sciences Combinatorics Class relations Congruence permutability Congruence modularity Equivalence relation Congruence (manifolds) 0101 mathematics Algebra over a field Directly decomposable congruence classes Egg-box property Class relations Congruence permutability Congruence distributivity Congruence modularity Directly decomposable congruence classes Difunctionality Egg-box property Mal’tsev condition Mal’tsev variety Shifting lemma Mathematics Algebra and Number Theory Binary relation 010102 general mathematics Congruence distributivity Join (topology) Difunctionality Mal'tsev variety 010201 computation theory & mathematics Shifting lemma Variety (universal algebra) |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| Popis: | 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 |
| Databáze: | OpenAIRE |
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