# Differences

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congruence_distributive [2010/08/20 19:59] jipsen created |
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. | ||

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