=====Congruence distributivity=====

An algebra is \emph{congruence distributive} (or CD for short) if its lattice of congruence relations is a [[distributive lattices|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 [(Bjarni Jónsson, \emph{Algebras whose congruence lattices are distributive},
Math. Scand., \textbf{21}, 1967, 110--121 [[http://www.ams.org/mathscinet-getitem?mr=38:5689|MRreview]])] which implies that a finitely
generated CD variety is residually finite.


=== Properties that imply congruence distributivity ===

[[Equationally def. pr. cong.]]

=== Properties implied by congruence distributivity ===

[[Congruence modular]]