Congruence distributivity

An algebra is congruence distributive (or CD for short) if its lattice of congruence relations is a distributive lattice.

A class of algebras is congruence distributive if each of its members is congruence distributive.

Congruence distributivity has many structural consequences. The most striking one is perhaps Jónsson's Lemma 1) which implies that a finitely generated CD variety is residually finite.

Properties that imply congruence distributivity

Properties implied by congruence distributivity

1) Bjarni Jónsson, Algebras whose congruence lattices are distributive, Math. Scand., 21, 1967, 110–121 MRreview