A note on multiplicative primeness of prime degenerate Jordan algebras
type: Item
instance of: scholarly article
title: A note on multiplicative primeness of prime degenerate Jordan algebras
zbMATH Open document ID: 1208.17023
author: J. C. Cabello
author: R. Roura
author: M. Cabrera
published in: Siberian Mathematical Journal
publication date: 2010-12-08T00:00:00Z
review text: An algebra \(A\) is called prime if, given two nonzero ideals \(U\) and \(V\) of \(A\), always \(UV\not=0\). It is well-known that the multiplication algebra \(M(A)\) of a prime algebra need not be a prime algebra. An algebra \(A\) is called multiplicatively prime (m. p.) if both \(A\) and \(M(A)\) are prime algebras. The authors show the primeness of the multiplication algebra of the two algebras introduced by \textit{V. G. Skosyrskii} [Algebra Logic 33, No. 3, 169--179 (1994); translation from Algebra Logika 33, No. 3, 301--316 (1994; Zbl 0826.17037)]. It is shown that the Jordan algebra \(J(G,\delta)\) obtained from the Grassmann algebra by replacing its associate product with a new one defined using odd derivations of \(G\) is a multiplicatively prime degenerate Jordan algebra, and that the Jordan algebra \(J(G,D)\) obtained from the Grassmann algebra by replacing its associate product with a new one defined using even derivations of \(G\) is a multiplicatively prime degenerate Jordan algebra as well.
reviewed by: Susanne Pumplün
Mathematics Subject Classification ID: 17C10
zbMATH DE Number: 5824084
zbMATH Keywords: prime degenerate Jordan algebra
zbMATH Keywords: Kantor construction
zbMATH Keywords: Jordan superalgebra
zbMATH Keywords: multiplicatively prime algebra
MaRDI profile type: Publication
full work available at URL: s11202-010-0082-8
OpenAlex ID: W2036615698
cites work: Multiplicative-Semiprimeness of Nondegenerate Jordan Algebras
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cites work: Q4865491
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cites work: Q4006530
cites work: The radical of a non-associative algebra
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DOI: 10.1007/S11202-010-0082-8
description: scientific article; zbMATH DE number 5824084