**This is an old revision of the document!**

## Congruence e-regularity

An algebra with a constant term $e$ is ** congruence $e$-regular** if each congruence relation of the algebra is
determined by its $e$-congruence class, i.e., for all congruences $\theta$, $\psi$ of the algebra
$[e]_{\theta}=[e]_{\psi}\implies
\theta =\psi$.

A class of algebras is ** congruence $e$-regular** if each of its members is congruence $e$-regular for a fixed constant term $e$ in
the language of the class.

Congruence $e$-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_e-regular