IJPAM: Volume 93, No. 1 (2014)

ON GENERALIZED DERIVATIONS OF SEMIPRIME RINGS

Asma Ali$^1$, Faiza Shujat$^2$
$^{1,2}$Department of Mathematics
Aligarh Muslim University
Aligarh, 202002, INDIA


Abstract. Let $R$ be a ring and $S$ be a nonempty subset of $R$. A
mapping $f:R\longrightarrow R$ is said to be centralizing (resp. commuting) on $S$ if $[x, f(x)]\in Z(R)$ (resp. $[x, f(x)]=0$) for all $x\in S$. The purpose of this paper is to generalize the classical theorem of Posner [7, Theorem 2] and to extend a result of Bell and Martindale [1, Theorem 3] for a generalized derivation of a semiprime ring $R$ which is commuting on a left ideal of $R$.

Received: December 17, 2011

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DOI: 10.12732/ijpam.v93i1.1 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 1
Pages: 1 - 5

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).