Composition algebras over rings of fractions revisited
type: Item
instance of: scholarly article
title: Composition algebras over rings of fractions revisited
zbMATH Open document ID: 0973.17004
author: Susanne Pumplün
published in: Journal of Algebra
publication date: 2001-12-02T00:00:00Z
review text: For \(k\) a field of characteristic not two, let \(f_h (x_0,x_1)\in k[x_0,x_1]\) denote an irreducible homogeneous polynomial and the ring of elements of degree zero in the homogeneous localization \(k[x_0,x_1]_{f_h}\) is denoted by \(k[x_0,x_1]_{(f_h)}\). For \(\text{deg}f_h=3\) the author proves that the composition algebras over \(k[x_0,x_1]_{(f_h)}\) not containing zero divisors are defined over \(k\) and that there is at most one (split) composition algebra not defined over \(k\). For \(\text{deg}f_h=4\) all composition algebras over \(k[x_0,x_1]_{(f_h)}\) are enumerated and partly classified.
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 17A75
zbMATH DE Number: 1211658
MaRDI profile type: Publication
full work available at URL: jabr.1997.7263
OpenAlex ID: W1968129864
cites work: Q4143433
cites work: Q3997794
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cites work: Composition Algebras Over Algebraic Curves of Genus Zero
cites work: Composition algebras over rings of genus zero
cites work: Composition algebras over a ring of fractions
cites work: Q3708857
cites work: Cayley algebra bundles onA2K
DOI: 10.1006/JABR.1997.7263
description: scientific article; zbMATH DE number 1211658