Congruence properties in congruence permutable and in ideal determined varieties, with applications. |
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Authors: | C J van Alten |
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Institution: | (1) School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits, 2050, South Africa |
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Abstract: | We define a weak version of EDPC (equationally definable principal congruences), called EDPC*, that is shown to be preserved under varietal closure in congruence permutable varieties. We show that if
is a congruence permutable variety generated by a class
then
has EDPC iff
has EDPC* iff
has EDPC*. An equational condition is given which, if satisfied by
implies that
has the CEP (congruence extension property). Similar results are proved for ideal determined varieties. These results are applied to the variety of residuated lattices, with examples.Received January 15, 2004; accepted in final form October 8, 2004. |
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Keywords: | 08B99 06B10 |
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