Congruence-modular variety

Summary

A congruence-modular variety is a variety in which the congruence lattice of every algebra is a modular lattice. It includes every congruence-permutable variety, such as groups, rings and modules, and every congruence-distributive variety, such as lattices. Congruence-modular varieties are the natural setting of commutator theory, which brings ideas of group theory to general algebras.