## 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,

**, Math. Scand.,**

*Algebras whose congruence lattices are distributive***21**, 1967, 110–121 MRreview

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