## Congruence distributivity

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

A class of algebras is \emph{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, \emph{Algebras whose congruence lattices are distributive}, Math. Scand., \textbf{21}, 1967, 110–121 MRreview