On polynomial identities in associative and Jordan pairs
type: Item
instance of: scholarly article
title: On polynomial identities in associative and Jordan pairs
zbMATH Open document ID: 1239.17026
author: Fernando Montaner
author: Irene Paniello
published in: Algebras and Representation Theory
publication date: 2010-04-21T00:00:00Z
review text: In this paper the authors prove that a Jordan system (pair or triple system) \(J\) satisfies a polynomial identity (PI) if and only if it satisfies a homotope PI, i.e. a PI which holds in all the homotopes of \(J\). The core of the proof, based on structure theory, is the following analogue of Amitsur's theorem on associative algebras with involution satisfying a *-PI: If \(A\) is a primitive associative pair with involution * such that the Jordan pair of the Hermitian elements \(H(A,{}^*)\) satisfies a PI, then \(A\) is simple of finite capacity. The paper concludes by stating improvements on already-proved Jordan analogues of Kaplansky's and Posner-Rowen's theorems on primitive and prime PI-algebras.
reviewed by: Antonio Fernández López
Mathematics Subject Classification ID: 17C10
Mathematics Subject Classification ID: 17A40
Mathematics Subject Classification ID: 16R20
zbMATH DE Number: 5696489
zbMATH Keywords: Jordan pair
zbMATH Keywords: homotope polynomial identity
zbMATH Keywords: involutions
MaRDI profile type: Publication
full work available at URL: s10468-008-9114-5
OpenAlex ID: W2077486476
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DOI: 10.1007/S10468-008-9114-5
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description: scientific article; zbMATH DE number 5696489