It is shown that a variety V has distributive congruence lattices if and only if the intersection of two principal congruence relations is definable by equations involving terms with parameters. The nature of the terms involved then provides a useful classification of congruence distributive varieties. In particular, the classification puts into proper perspective two stronger properties. A variety is said to have the Principal Intersection Property if the intersection of any two principal congruence relations is principal, or the Compact Intersection Property if the intersection of two compact congruence relations is compact. For non-congruence-distributive varieties, it is shown that some useful constructions are nevertheless possible.

Aglianò, P., Baker, K.A. (1999). Congruence intersection properties for varieties of algebras. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 67(1), 104-121 [10.1017/s1446788700000896].

Congruence intersection properties for varieties of algebras

Aglianò, P.;
1999-01-01

Abstract

It is shown that a variety V has distributive congruence lattices if and only if the intersection of two principal congruence relations is definable by equations involving terms with parameters. The nature of the terms involved then provides a useful classification of congruence distributive varieties. In particular, the classification puts into proper perspective two stronger properties. A variety is said to have the Principal Intersection Property if the intersection of any two principal congruence relations is principal, or the Compact Intersection Property if the intersection of two compact congruence relations is compact. For non-congruence-distributive varieties, it is shown that some useful constructions are nevertheless possible.
1999
Aglianò, P., Baker, K.A. (1999). Congruence intersection properties for varieties of algebras. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 67(1), 104-121 [10.1017/s1446788700000896].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1013883