Derivations cocentralizing multilinear polynomials
type: Item
instance of: scholarly article
title: Derivations cocentralizing multilinear polynomials
zbMATH Open document ID: 0885.16022
author: Tsai-Lien Wong
published in: Taiwanese Journal of Mathematics
publication date: 1998-04-06T00:00:00Z
review text: The main result of this paper shows that if \(R\) is a prime \(K\) algebra, \(f(X_1,\dots,X_n)\) is a multilinear and homogeneous polynomial over \(K\) in noncommuting variables, \(D\) and \(E\) are derivations of \(R\), and \(D(f(y_1,\dots,y_n))f(y_1,\dots,y_n)-f(y_1,\dots,y_n)E(f(y_1,\dots,y_n))\) is central for all \(y_i\in I\), a nonzero ideal of \(R\), then either \(D=E=0\), or \(E=-D\) and \(f(X_1,\dots,X_n)^2\) is central valued on \(R\), except when \(\text{char} R=2\) and \(R\) satisfies the standard identity \(S_4\).
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16R50
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16U70
zbMATH DE Number: 1054446
zbMATH Keywords: prime algebras
zbMATH Keywords: multilinear homogeneous polynomials
zbMATH Keywords: derivations
zbMATH Keywords: standard identities
reviewed by: Charles Lanski
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500404923
OpenAlex ID: W4245293398
DOI: 10.11650/TWJM/1500404923
description: scientific article; zbMATH DE number 1054446