Document Details Document Type : Article In Journal  Document Title : On Lie ideals and generalized (theta,phi)-derivations in prime rings On Lie ideals and generalized (theta,phi)-derivations in prime rings   Document Language : Arabic  Abstract : Let R be a prime ring with characteristic different from two and S a non-empty subset of R. Suppose that theta, phi are endomorphisms of R. An additive mapping F : R --> R is called a generalized (theta, phi)-derivation (resp. generalized Jordan (theta, phi)-derivation) on S if there exists a (theta, phi)-derivation d : R --> R such that F(xy) = F(x)theta(y) + phi(x)d(y) (resp. F(x(2)) = F(x)(x) + phi(x)d(x)), holds for all x, y epsilon S. Suppose that U is a Lie ideal of R such that u(2) epsilon U, for all u epsilon U. In the present paper, it is shown if theta is an automorphism of R then every generalized Jordan (theta, phi)-derivation F on U is a generalized (theta, phi)-derivation on U.  Journal Name : COMMUNICATIONS IN ALGEBRA  Volume : 32  Issue Number : 8  Publishing Year : 2004 AH   Added Date : Friday, June 20, 2008  Researchers Researcher Name (Arabic) Researcher Name (English) Researcher Type Dr Grade Email أشرف مبارز زنقور Ashraf M Researcher     . Ali A Researcher     . Ali S Researcher     Back To Researches Page