Reduced simple Jordan algebras of degree three over a field with a discrete valuation
type: Item
instance of: scholarly article
title: Reduced simple Jordan algebras of degree three over a field with a discrete valuation
zbMATH Open document ID: 0349.17008
DOI: 10.1007/BF01238733
author: Holger P. Petersson
published in: Archiv der Mathematik
publication date: 1974-01-01T00:00:00Z
review text: Let \(k\) be a complete discrete valuation field, \(\tilde k\) its residue class field. The author obtains necessary and sufficient conditions for isomorphism of reduced central simple Jordan algebras of degree three over \(k\) in terms of \(\tilde k\) data, assuming the absence of certain pathologies which may occur if \(\tilde k\) is of characteristic two. \textit{T. A. Springer}'s first and second residue forms [Nederl. Akad. Wet., Proc., Ser. A 58, 352--362 (1955; Zbl 0067.27605)] and the author's results on composition algebras over \(k\) [J. Algebra 29, 414--426 (1974; Zbl 0291.17013)] are used to study the quadratic forms \(T(x^\sharp)\) in Springer's criterion on isomorphism [the reviewer, Trans. Am. Math. Soc. 164, 93--103 (1972; Zbl 0236.17007)].
Mathematics Subject Classification ID: 17C10
zbMATH DE Number: 3544235
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01238733
OpenAlex ID: W2079391568
description: scientific article; zbMATH DE number 3544235