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Separation of clones by means of hyperidentities. (English. Russian original) Zbl 0854.08003

Sib. Math. J. 35, No. 2, 280-285 (1994); translation from Sib. Mat. Zh. 35, No. 2, 310-316 (1994).
It was shown by K. Denecke, D. Lau, R. Pöschel and D. Schweigert [Contrib. Gen. Algebra 7, 97-118 (1991; Zbl 0759.08005)] that, given two nonisomorphic clones \(C\) and \(C'\) of Boolean functions with \(C'\not\cong C\), \(C'\nsubseteq C\), and \(C\nsubseteq C'\), the clone \(C\) can be separated from \(C'\) by hyperidentities. This fact is not true for arbitrary clones of functions defined on a finite set with more than two elements. In this paper we give a more general criterion for separation of clones by means of hyperidentities and we use this result to obtain a new proof of the theorem stating that Boolean clones can be separated by hyperidentities.

MSC:

08A40 Operations and polynomials in algebraic structures, primal algebras

Citations:

Zbl 0759.08005
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References:

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