Affine spaces over GF(4)
type: Item
instance of: scholarly article
title: Affine spaces over GF(4)
zbMATH Open document ID: 0901.08007
DOI: 10.1007/BF01236757
author: Józef Dudek
author: Jerzy Tomasik
published in: Algebra Universalis
publication date: 1998-11-24T00:00:00Z
review text: An algebra \(A\) is said to represent the sequence \((p_0,p_1,\dots)\) if the number of essentially \(n\)-ary term operations in \(A\) is equal to \(p_n\). It was shown by \textit{G. Grätzer} and \textit{R. Padmanabhan} [Proc. Am. Math. Soc. 28, 75-80 (1971; Zbl 0215.34501)] that \((G,\cdot)\) is a nontrivial affine space over \(GF(3)\) if and only if \((G,\cdot)\) represents the sequence \((0,1,1,3,5).\) The authors prove the following Theorem: A groupoid \((G,\cdot)\) is a nontrivial affine space over \(GF(4)\) if and only if \((G,\cdot)\) represents the sequence \((0,1,2,7)\).
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08A62
Mathematics Subject Classification ID: 20N02
Mathematics Subject Classification ID: 08A40
zbMATH DE Number: 1226544
zbMATH Keywords: representable sequence
zbMATH Keywords: affine space over GF(p)
zbMATH Keywords: groupoid
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01236757
OpenAlex ID: W1980804633
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description: scientific article; zbMATH DE number 1226544