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Tolerances in congruence permutable algebras. (English) Zbl 0678.08004
A variety V is tolerance trivial iff it is congruence permutable. Hence, investigations on tolerances are reasonable only in congruence non- permutable varieties. But, is this true also for single algebras? The author shows a modular lattice which is congruence permutable but not tolerance trivial and a lattice which is congruence permutable, non- simple and tolerance non-trivial.
With respect to these examples, we have the following question: Does there exist a congruence permutable algebra A which is not tolerance trivial and Con(A) is not a chain? The author shows that there exists a congruence permutable lattice which is tolerance permutable and not tolerance trivial and whose congruence lattice is not a chain.
Reviewer: A.Hatvany

MSC:
08B10 Congruence modularity, congruence distributivity
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References:
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