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congruence_modular [2010/08/20 20:05]
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Congruence modularity holds for many 'classical' varieties such as groups and rings. Congruence modularity holds for many 'classical' varieties such as groups and rings.
-A Mal'cev condition (with 4-ary terms) for congruence modularity is given by [(Alan Day, \emph{A characterization of modularity for congruence lattices of algebras.},  +A Mal'cev condition (with 4-ary terms) for congruence modularity is given by Alan Day, \emph{A characterization of modularity for congruence lattices of algebras.},  
-Canad. Math. Bull., \textbf{12}, 1969, 167-173 [[http://www.ams.org/mathscinet-getitem?mr=40:1317|MRreview]])]+Canad. Math. Bull., \textbf{12}, 1969, 167-173 [[http://www.ams.org/mathscinet-getitem?mr=40:1317|MRreview]]
-Another Mal'cev condition (with ternary terms) for congruence modularity is given by [(H.-Peter Gumm, \emph{Congruence modularity is permutability composed with distributivity},  +Another Mal'cev condition (with ternary terms) for congruence modularity is given by H.-Peter Gumm, \emph{Congruence modularity is permutability composed with distributivity},  
-Arch. Math. (Basel), \textbf{36}, 1981, 569-576 [[http://www.ams.org/mathscinet-getitem?mr=82j:08009|MRreview]])]+Arch. Math. (Basel), \textbf{36}, 1981, 569-576 [[http://www.ams.org/mathscinet-getitem?mr=82j:08009|MRreview]]
-Several further characterizations are given in [(Steven T. Tschantz, \emph{More conditions equivalent to congruence modularity}, +Several further characterizations are given by Steven T. Tschantz, \emph{More conditions equivalent to congruence modularity},
Universal algebra and lattice theory (Charleston, S.C., 1984), Universal algebra and lattice theory (Charleston, S.C., 1984),
Lecture Notes in Math. Lecture Notes in Math.
-\textbf{1149}, 1985, 270-282,  [[http://www.ams.org/mathscinet-getitem?mr=87e:08009|MRreview]])]+\textbf{1149}, 1985, 270-282,  [[http://www.ams.org/mathscinet-getitem?mr=87e:08009|MRreview]]
=== Properties that imply congruence modularity === === Properties that imply congruence modularity ===