6533b822fe1ef96bd127d87d

RESEARCH PRODUCT

Triangular irreducibility of congruences in quasivarieties

Janusz Czelakowski

subject

Section (fiber bundle)Mathematics::LogicPure mathematicsAlgebra and Number TheoryQuasivarietyIntegerMathematics::General MathematicsMathematics::Rings and AlgebrasMathematics::General TopologyIrreducibilityFinitely-generated abelian groupCongruence relationMathematics

description

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.

yearjournalcountryeditionlanguage
2014-03-25Algebra Universalis
10.1007/s00012-014-0274-3http://link.springer.com/article/10.1007/s00012-014-0274-3