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LIE IDEALS AND GENERALIZED JORDAN SEMIDERIVATIONS
Author :
Gülten Erol & Oznur Golba¸Si
Corresponding Author:
Oznur Golba¸Si
Email
ogolbasi@cumhuriyet.edu.tr
Section :
Research Paper
Country :
Turkey
Keywords :
Prime rings, Semiderivations, Generalized semiderivations, Lie ideals.
Abstract :
Let R be an associative ring. An additive mapping f : R ! R is called a generalized semiderivation if there exists a semiderivation d associated with map g such that (i) f (xy) = f (x)y + g(x)d(y) = f (x)g(y) + xd(y); (ii) f (g(x)) = g(f (x)); for all x; y 2 R: In this paper, we prove that if R is a prime ring with characteristic deferent from two, g an endomorphism of R; f a generalized Jordan semiderivation associated with d and g on a Lie ideal of R; then f is a generalized semiderivation and d is a semiderivation on a nonzero Lie ideal of R:
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