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Conditions for trivial principal tolerances. (English) Zbl 0538.08002
By a tolerance on an algebra A is meant a compatible reflexive and symmetric relation on A. By a principal tolerance T(a,b) on A is meant the least tolerance on A containing the pair \(<a,b>\) of elements of A. An algebra A has trivial principal tolerances if every T(a,b) is a congruence on A. The paper contains two characterizations of varieties of algebras with trivial principal tolerances; the first one is formulated in terms of the relational product, the other in polynomial conditions.
Reviewer: I.Chajda

MSC:
08A30 Subalgebras, congruence relations
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