## Congruence regularity

An algebra is ** 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 ** 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 …

Trace: » congruence_regular