Generalized derivations and left multipliers on Lie ideals |
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Authors: | Basudeb Dhara Vincenzo De Filippis Rajendra K Sharma |
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Institution: | 1.Department of Mathematics,Belda College,Belda, Paschim Medinipur,India;2.DI.S.I.A., Faculty of Engineering,University of Messina,Messina,Italy;3.Department of Mathematics,Indian Institute of Technology, Delhi,New Delhi,India |
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Abstract: | Let m, n be two fixed positive integers and let R be a 2-torsion free prime ring, with Utumi quotient ring U and extended centroid C. We study the identity F(x
m+n+1) = F(x)x
m+n
+ x
m
D(x)x
n
for x in a non-central Lie ideal of R, where both F and D are generalized derivations of R and then determine the relationship between the form of F and that of D. In particular the conclusions of the main theorem say that if D is the non-zero map in R, then R satisfies the standard identity s
4(x
1, . . . , x
4) and D is a usual derivation of R. |
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Keywords: | |
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