Affine spaces over GF(3)
type: Item
instance of: scholarly article
title: Affine spaces over GF(3)
zbMATH Open document ID: 1019.08001
DOI: 10.1023/A:1021893307315
author: Józef Dudek
published in: Studia Logica
publication date: 2003-04-27T00:00:00Z
review text: For an algebra \textbf{A}, \(p_n({\mathbf A})\) denotes the number of essentially \(n\)-ary term functions over \textbf{A}. It was shown by \textit{G. Grätzer} and \textit{R. Padmanabhan} [Proc. Am. Math. Soc. 28, 75-80 (1971; Zbl 0215.34501)] that an algebra \textbf{A} is a nontrivial affine space over GF(3) if and only if \(p_n({\mathbf A})=(2^n-(-1)^n)/3\) for \(n=1,2,\dots\). The author of this paper gives various results where extra conditions on \textbf{A} enable a weakening of the conditions on \(p_n({\mathbf A})\). The particular result given in this note is that an idempotent algebra \((G,s)\) of type (3) is a nontrivial affine space over GF(3) if and only if \(p_4(G,s)=5\).
reviewed by: Sheila Oates-Williams
Mathematics Subject Classification ID: 08A05
zbMATH DE Number: 1901332
zbMATH Keywords: \(p_n\)-sequence
zbMATH Keywords: affine spaces
MaRDI profile type: Publication
full work available at URL: a:1021893307315
OpenAlex ID: W3161389373
description: scientific article; zbMATH DE number 1901332