Congruence regularity

An algebra is \emph{congruence regular} if each congruence relation of the algebra is determined by any one of its congruence classes, i.e. $\forall a,b\ [a]_{\theta}=[b]_{\psi}\Longrightarrow \theta =\psi$.

A class of algebras is \emph{congruence regular} if each of its members is congruence regular.

Congruence regularity holds for many 'classical' varieties such as groups, rings and vector spaces.

This property can be characterized by a Mal'cev condition …

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