A characterization of Sheffer functions by hyperidentities
type: Item
instance of: scholarly article
title: A characterization of Sheffer functions by hyperidentities
zbMATH Open document ID: 0642.08002
DOI: 10.1007/BF02573146
author: Klaus Denecke
author: Reinhard Pöschel
published in: Semigroup Forum
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134937
review text: A Sheffer function is a function f: A \(n\to A\) such that the algebra \b{A}\(=<A;f>\) is primal. A hyperidentity for a universal algebra \b{A} is an identity for its clone of operations. The paper gives a new primality criterion, i.e. a characterization of Sheffer functions in terms of hyperidentities: If \(| A|\) is a prime power, then f: A \(n\to A\) is a Sheffer function iff the algebra \b{A}\(=<A;f>\) satisfies neither of two given unary hyperidentities. The cases \(| A| \in \{2,3,4\}\) are treated as examples.
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 20M20
zbMATH DE Number: 4045813
zbMATH Keywords: primal algebra
zbMATH Keywords: Sheffer function
zbMATH Keywords: hyperidentity
zbMATH Keywords: universal algebra
zbMATH Keywords: clone of operations
zbMATH Keywords: primality criterion
MaRDI profile type: Publication
cites work: Q5507586
cites work: Q5515373
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cites work: Q3337385
cites work: Completeness in Finite Algebras with a Single Operation
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description: scientific article; zbMATH DE number 4045813