Regularity in arithmetical varieties. (English) Zbl 0573.08004

Chajda, Ivan

Arch. Math., Brno 20, 177-182 (1984).

An algebra is regular if any congruence is uniquely determined by anyone of its congruence classes. The paper gives a Mal’cev condition characterizing both arithmeticity \((=congruence\) distributivity and congruence permutability) and regularity in a form different from the conjunction of known Mal’cev conditions for separated properties and which is of special interest in varieties with an associative binary operation or with a special Pixley polynomial.

Reviewer: J.Duda

MSC:

08B05	Equational logic, Mal’tsev conditions
08B10	Congruence modularity, congruence distributivity

Keywords:

Mal’cev condition; arithmeticity; regularity; varieties; Pixley polynomial