\(*\)-differential identities of semiprime rings with involution
type: Item
instance of: scholarly article
title: \(*\)-differential identities of semiprime rings with involution
zbMATH Open document ID: 0862.16016
author: Tadashi Yanai
published in: Journal of Algebra
publication date: 1997-05-26T00:00:00Z
review text: Various results in the literature show that differential identities of a ring \(R\) arise from generalized polynomial identities of \(R\), when \(R\) is a semiprime ring, or is a prime ring with involution. The author extends these results to identities of semiprime rings with involution. Let \(R\) be a semiprime ring with involution * and with characteristic \(\neq 2\). If \(\{\Delta_j\}\) are certain ``reduced'' words in the derivations of \(R\), and if \(f(x_i^{\Delta_j},(x_i^{\Delta_j})^*)\) is a *-differential identity for \(R\), the author proves that \(R\) satisfies the *-generalized identity \(f(z_{ij}e(\Delta_j),(z_{ij}e(\Delta_j))^*)\), where \(e(\Delta_j)\) are idempotents in the extended centroid of \(R\), and \(\{z_{ij}\}\) are indeterminates. The proof uses the notion of orthogonal completeness.
Mathematics Subject Classification ID: 16R50
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 16N60
zbMATH DE Number: 954752
zbMATH Keywords: differential identities
zbMATH Keywords: generalized polynomial identities
zbMATH Keywords: semiprime rings with involution
zbMATH Keywords: derivations
zbMATH Keywords: idempotents
zbMATH Keywords: extended centroid
zbMATH Keywords: orthogonal completeness
reviewed by: Charles Lanski
MaRDI profile type: Publication
full work available at URL: jabr.1996.0372
OpenAlex ID: W1982476069
DOI: 10.1006/JABR.1996.0372
description: scientific article; zbMATH DE number 954752