The kernel and range inclusions of integral derivations in semiprime rings.
type: Item
instance of: scholarly article
title: The kernel and range inclusions of integral derivations in semiprime rings.
zbMATH Open document ID: 1158.16018
author: Chen-Lian Chuang
author: Tsiu-Kwen Lee
author: Tsai-Lien Wong
published in: Journal of Algebra
publication date: 2008-12-02T00:00:00Z
review text: Let \(R\) be a semiprime ring with extended centroid \(C\), symmetric Martindale quotient ring \(Q\), and essential ideal \(I\). For any \(C\)-integral derivation \(D\) of \(R\), by the theory of differential identities, there is an associated inner derivation \(ad(a)\) for \(a\in Q\). For any other derivation \(\delta\) of \(R\), the authors characterize the inclusion of the images of \(D\) and \(\delta\), and of their kernels. Specifically they prove that \(\{x\in I\mid D(x)=0\}\subseteq\{x\in I\mid\delta(x)=0\}\) if and only if \(\delta=c_nD^n+\cdots+c_1D+ad(b)\) for some \(n\geq 1\), \(c_i\in C\), \(b\in C[a]\), and that \(\delta(I)\subseteq D(I)\) if and only if the last relation above holds with \(\sum_{i\geq 1}(-1)^iD^i(c_i)=0\).
reviewed by: Charles Lanski
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16N60
zbMATH DE Number: 5376928
zbMATH Keywords: integral derivations
zbMATH Keywords: semiprime rings
zbMATH Keywords: range inclusions
zbMATH Keywords: kernel inclusions
zbMATH Keywords: differential identities
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.06.026
OpenAlex ID: W2080083346
Wikidata QID: Q57788073
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DOI: 10.1016/J.JALGEBRA.2008.06.026
description: scientific article; zbMATH DE number 5376928