Congruence distributive

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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 [Bjarni Jónsson, Algebras whose congruence lattices are distributive, Math. Scand. 21 (1967) 110--121 (1968) MRreview] which implies that a finitely generated CD variety is residually finite.

Properties that imply congruence distributivity

Equationally definable principal congruences

Properties implied by congruence distributivity

Congruence modular