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

QR Code
QR Code congruence_distributive (generated for current page)