Derivations cocentralizing polynomials
type: Item
instance of: scholarly article
title: Derivations cocentralizing polynomials
zbMATH Open document ID: 0927.16032
author: Tsiu-Kwen Lee
author: Wen-Kwei Shiue
published in: Taiwanese Journal of Mathematics
publication date: 1999-12-12T00:00:00Z
review text: The authors prove the following theorem: Let \(R\) be a prime ring with extended centroid \(C\), let \(D\) and \(E\in\text{Der}(R)\), and let \(f(X_1,\dots,X_t)\in C\{X_1,\dots,X_t\}\) and not central valued on \(R\). If for all \(r_i\in R\), \(D(f(r_i))f(r_i)-f(r_i)E(f(r_i))\in C\) then either \(D=E=0\), or \(E=-D\) and \(f(X_i)^2\) is central valued on \(R\), except when \(\text{char }R=2\) and \(\dim_C RC=4\). This result generalizes the corresponding one for a multilinear polynomial \(f(X_j)\) proved by \textit{T.-L. Wong} [Taiwanese J. Math. 1, No. 1, 31-37 (1997; Zbl 0885.16022)].
reviewed by: Charles Lanski
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16R50
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16U80
zbMATH DE Number: 1269915
zbMATH Keywords: derivations
zbMATH Keywords: prime rings
zbMATH Keywords: extended centroids
zbMATH Keywords: multilinear polynomials
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500407017
OpenAlex ID: W1852820979
DOI: 10.11650/TWJM/1500407017
description: scientific article; zbMATH DE number 1269915