IJPAM: Volume 106, No. 1 (2016)

ON MULTIPLICATIVE (GENERALIZED)-DERIVATIONS
IN SEMIPRIME RINGS

Deepak Kumar$^1$, Gurninder S. Sandhu$^2$
$^{1,2}$Department of Mathematics
Punjabi University
Patiala, 147002, INDIA


Abstract. Let R be a ring. A map $F:R\rightarrow R$ (not necessarily additive) is called a multiplicative (generalized)-derivation of R if $F(xy)=F(x)y+xf(y)$ for all $x,y\in$ R, where $f:R\rightarrow R$ is any map (not necessarily a derivation nor additive). The main purpose of this paper is to study the following situations (i) $F[x,y]\pm xy=0$ (ii) $F[x,y]\pm yx=0$ (iii) $F(x\circ y)\pm xy=0$ (iv) $F(x\circ y)\pm yx=0$ (v) $f(x)F(y)\pm xy=0$ (vi) $f(x)F(y)\pm yx=0$ (vii) $[F(x),y]\pm x\circ G(y)=0$ (viii) $F(x)\circ y\pm x\circ G(y)=0$, for all $x,y$ in some appropriate subsets of R.

Received: October 15, 2015

AMS Subject Classification: 16W25, 16R50, 16N60

Key Words and Phrases: semiprime ring, left ideal, two sided ideal, derivation, multiplicative derivation, multiplicative (generalized)-derivation

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DOI: 10.12732/ijpam.v106i1.19 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: 2016
Volume: 106
Issue: 1
Pages: 249 - 257


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