Ideals and the binary discriminator in universal algebra. (English) Zbl 0979.08001

The role of the ternary discriminator (and the ternary dual discriminator) in universal algebra is well known. The authors of the paper introduce, for algebras with \(0\), the notions of the binary discriminator and the dual binary discriminator and study the importance of these functions for \(0\)-versions of properties (such as permutability, arithmeticity and distributivity) of varieties of algebras with \(0\). For finite algebras the dual discriminator is described as the intersection of maximal subclones of a clone. Furthermore, using also the notions of an ideal of an algebra with \(0\), binary and dual binary discriminator algebras and varieties are characterized.


08A05 Structure theory of algebraic structures
08B05 Equational logic, Mal’tsev conditions
08B10 Congruence modularity, congruence distributivity
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