Key words: Algebra with 0, variety with 0, ideal, ternary and binary discriminator and dual discriminator, 0-primal algebras, binary discriminator and binary dual discriminator varieties.
Springer Online Journal Archives 1860-2000
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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