Generalized derivations with nilpotent values on semiprime rings.
type: Item
instance of: scholarly article
title: Generalized derivations with nilpotent values on semiprime rings.
zbMATH Open document ID: 1064.16036
author: Feng Wei
publication date: 2004-10-01T00:00:00Z
review text: This paper concerns a generalized derivation \(g\colon I\to R\) for \(R\) a semiprime ring, \(I\) an essential ideal of \(R\), and \(d\colon I\to R\) the derivation associated to \(g\). The main results show that \(g\) extends to a generalized derivation of the left Martindale quotient ring \(R_F\) of \(R\) and has the form \(g(x)=ax+d(x)\) for some \(a\in R_F\), \(d\) a derivation of \(R_F\), and for all \(x\in R_F\). Also if \(g(x)^n=0\) for all \(x\in I\) then \(g=0\). The crucial Theorem 5 in the paper is incomplete since the reference at the end of its proof does not apply. A complete argument for this result appears in [\textit{T.-K. Lee}, Commun. Algebra 27, No. 8, 4057-4073 (1999; Zbl 0946.16026)]. This paper of Lee also contains the main results here but for the somewhat more general situation when \(I\) is a dense right ideal of \(R\).
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16N60
zbMATH DE Number: 2104903
zbMATH Keywords: semiprime rings
zbMATH Keywords: generalized derivations
zbMATH Keywords: Martindale quotient rings
reviewed by: Charles Lanski
MaRDI profile type: Publication
full work available at URL: s10114-004-0318-2
OpenAlex ID: W2315599534
cites work: Generalized derivations in rings*
cites work: Derivations with nilpotent values
cites work: Q4011053
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cites work: Derivations in Prime Rings
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cites work: Derivations of prime rings
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DOI: 10.1007/S10114-004-0318-2
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2104903