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congruence_distributive [2010/08/20 19:59]
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congruence_distributive [2010/08/20 20:01] (current)
jipsen
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-=====Congruence distributive=====+=====Congruence distributivity=====
An algebra is \emph{congruence distributive} (or CD for short) if its lattice of congruence relations is a [[distributive lattices|distributive lattice]]. An algebra is \emph{congruence distributive} (or CD for short) if its lattice of congruence relations is a [[distributive lattices|distributive lattice]].
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A class of algebras is \emph{congruence distributive} if each of its members is congruence distributive. 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}, +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+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. generated CD variety is residually finite.