Topological \(J\)-divisors of zero in unitary \(p\)-normed Jordan algebras
type: Item
instance of: scholarly article
title: Topological \(J\)-divisors of zero in unitary \(p\)-normed Jordan algebras
zbMATH Open document ID: 0923.17029
DOI: 10.1023/A:1004593031219
author: N. El Yacoubi
author: H. Kemmoun
published in: Periodica Mathematica Hungarica
publication date: 1999-09-14T00:00:00Z
review text: For associative normed real algebras it is well-known [cf. \textit{I. Kaplansky}, Duke Math. J. 16, 399-418 (1949; Zbl 0033.18701)] that they are isomorphic to the real field, the complex field or the quaternions, if and only if they do not have non-trivial topological divisors of zero. This result was extended in the Jordan case by \textit{A. M. Kaïdi} [Ann. Sci. Univ. Blaise Pascal, Clermont II, Sér. Math. 27, 119-124 (1991; Zbl 0794.17001)]. In this paper the authors generalize these results in the case of \(p\)-normed Jordan algebras without non-trivial Jordan topological divisors of zero. In the complex case they prove that they are isomorphic to the complex field. In the real case they prove that they are quadratic division algebras (which may be of infinite dimension).
reviewed by: Bernard Aupetit
Mathematics Subject Classification ID: 17C50
Mathematics Subject Classification ID: 46H70
zbMATH DE Number: 1336363
zbMATH Keywords: Jordan algebras
zbMATH Keywords: \(p\)-normed Jordan algebras
zbMATH Keywords: Jordan topological divisors of zero
MaRDI profile type: Publication
full work available at URL: a:1004593031219
OpenAlex ID: W2207621323
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description: scientific article; zbMATH DE number 1336363