publication . Article . 2014

Triangular irreducibility of congruences in quasivarieties

Janusz Czelakowski;
Open Access English
  • Published: 25 Mar 2014 Journal: Algebra universalis, volume 71, issue 3, pages 261-283 (issn: 0002-5240, Copyright policy)
  • Publisher: Springer Nature
Abstract
Certain forms of irreducibility as well as of equational definability of relative congruences in quasivarieties are investigated. For any integer \({m \geqslant 3}\) and a quasivariety Q, the notion of an m-triangularily meet-irreducible Q-congruence in the algebras of Q is defined. In Section 2, some characterizations of finitely generated quasivarieties involving this notion are provided. Section 3 deals with quasivarieties with equationally definable m-triangular meets of relatively principal congruences. References to finitely based quasivarieties and varieties are discussed.
Subjects
arXiv: Mathematics::General TopologyMathematics::LogicMathematics::Rings and AlgebrasMathematics::General Mathematics
free text keywords: Algebra and Number Theory, Pure mathematics, Congruence relation, Discrete mathematics, Mathematics, Integer, Irreducibility, Quasivariety, Finitely-generated abelian group, Algebra
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