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A note on multiplicative (generalized) derivations with annihilator conditions

Basudeb Dhara and Krishna Gopal Pradhan

Abstract

Let R be a prime ring with center Z(R), aR (a ≠ 0) and I a nonzero ideal of R. Suppose that F,d:RR are any two mappings such that F(xy)=F(x)y+xd(y) for all x,yR. For all x,yI, we investigate the identities a(F(xy)±xy)=0, a(F(xy)±yx)=0, a(F(x)F(y)±xy)=0, a(F(x)F(y)±yx)=0, a(d(x)F(y)±xy)Z(R), a(d(x)F(y)±yx)Z(R) and a(F(xy)±F(x)F(y))=0.

The authors would like to thank the referee for providing very helpful comments and suggestions.

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Received: 2013-8-13
Revised: 2015-11-21
Accepted: 2016-2-26
Published Online: 2016-4-27
Published in Print: 2016-6-1

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