Abstract.
We introduce the binary discriminator and the dual binary discriminator and the corresponding universal algebras with 0. The latter are related to permutability and distributivity at 0. For A finite the dual binary discriminator is in the intersection of all maximal subclones of the clone of all f satisfying f (0,...,0) = 0 (except certain maximal subclones if A is of prime power cardinality). An algebra with a special binary term function and a special unary term function is a dual binary discriminator algebra if and only if it is ideal-free. Finally we characterize binary and dual binary discriminator varieties.
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Received April 3, 1997; accepted in final form July 28, 1998.
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Chajda, I., Halaš, R. & Rosenberg, I. Ideals and the binary discriminator in universal algebra. Algebra univers. 42, 239–251 (1999). https://doi.org/10.1007/s000120050001
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DOI: https://doi.org/10.1007/s000120050001