On (m, n)-derivations of Some Algebras

Let \(\mathcal{A}\) be a unital algebra, \(\delta\) be a linear mapping from \(\mathcal{A}\) into itself and \(m\), \(n\) be fixed integers. We call \(\delta\) an (\textit{m, n})-derivable mapping at \(Z\), if \(m\delta(AB)+n\delta(BA)=m\delta(A)B+mA\delta(B)+n\delta(B)A+nB\delta(A)\) for all \(A, B...

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Bibliographic Details
Published in:arXiv.org 2012-03
Main Authors: Li, Jiankui, Shen, Qihua, Guo, Jianbin
Format: Article
Language:English
Subjects:
Algebra
Integers
Mapping
Online Access:Get full text
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Summary:Let \(\mathcal{A}\) be a unital algebra, \(\delta\) be a linear mapping from \(\mathcal{A}\) into itself and \(m\), \(n\) be fixed integers. We call \(\delta\) an (\textit{m, n})-derivable mapping at \(Z\), if \(m\delta(AB)+n\delta(BA)=m\delta(A)B+mA\delta(B)+n\delta(B)A+nB\delta(A)\) for all \(A, B\in \mathcal{A}\) with \(AB=Z\). In this paper, (\textit{m, n})-derivable mappings at 0 (resp. \(I_\mathcal{A}\oplus0\), \(I\)) on generalized matrix algebras are characterized. We also study (\textit{m, n})-derivable mappings at 0 on CSL algebras. We reveal the relationship between this kind of mappings with Lie derivations, Jordan derivations and derivations.
ISSN:2331-8422