Congruence e-regular

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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 θ, ψ of the algebra [e]_θ = [e]_ψ ⇒ θ = ψ.

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 ...