Regularity in arithmetical varieties. (English) Zbl 0573.08004

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


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