Algebras with principal tolerances. (English) Zbl 0617.08012
A tolerance on an algebra A is a reflexive and symmetric binary relation on A having the substitution property with respect to the operations of A. An algebra is called tolerance principal if each of its finitely generated tolerances can be generated by one pair of elements, and a variety of algebras is termed tolerance principal if each of its members has this property. The author proves a polynomial characterization of tolerance principal varieties; as an example, he notes a peculiar variety of groupoids. A properly modified version of tolerance principalness for algebras with constants admits varieties of lattices with 0 or 1 as examples.
Reviewer: M.Armbrust
MSC:
| 08B10 | Congruence modularity, congruence distributivity |
| 08A30 | Subalgebras, congruence relations |
| 08B15 | Lattices of varieties |
References:
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