Discriminator polynomials and arithmetical varieties
type: Item
instance of: scholarly article
title: Discriminator polynomials and arithmetical varieties
zbMATH Open document ID: 0593.08005
DOI: 10.1007/BF01195145
published in: Algebra Universalis
publication date: 1985-01-01T00:00:00Z
review text: The author proves the following theorem: Given a locally finite semisimple arithmetical variety. For each natural number n there exists a term \(t_ n(x,y,z,u_ 1,...,u_ n)\) such that in any n-generated simple algebra, with generators \(s_ 1,...,s_ n\) the polynomial \(t_ n(x,y,z,s_ 1,...,s_ n)\) is a discriminator polynomial. A corollary of this is the result of A. Pixley saying that an arithmetical variety generated by a finite set K of finite simple algebras is a discriminator variety if and only if the members of K are hereditarily simple.
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 08A40
zbMATH DE Number: 3952839
zbMATH Keywords: locally finite semisimple arithmetical variety
zbMATH Keywords: discriminator polynomial
zbMATH Keywords: finite simple algebras
zbMATH Keywords: discriminator variety
author: Stanley N. Burris
reviewed by: Ervin Fried
MaRDI profile type: Publication
cites work: On the structure of varieties with equationally definable principal congruences. I
cites work: Q3934450
cites work: Connections between congruence-lattices and polynomial properties
cites work: Semi-categorial algebras. II
cites work: Completeness in arithmetical algebras
cites work: Eine Charakterisierung funktional vollständiger Algebren
cites work: Congruences on products of algebras and functionally complete algebras
full work available at URL: https://doi.org/10.1007/bf01195145
OpenAlex ID: W2027925226
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description: scientific article; zbMATH DE number 3952839