Some Theorems For Generalized (U,M)-Derivations In Semiprime Gamma-Rings
Keywords:Semiprime ?-ring, Lie ideal, Square closed Lie ideal, Admissible Lie ideal, -derivation, Generalized -derivation.
The objective of this paper is to establish some results for generalized (U,M)-derivation in semiprime Gamma-ring, where U is a Lie ideal of a semiprime Gamma-ring. Let d be a-(U,M)-derivation and f be a generalized (U,M)-derivation of M then we prove that
f(u?v)=f(u)?v+u?d(v) for all u,v belongs to U and a belongs to Gamma, when U is an admissible Lie ideal of M;
f(u?m)=f(u)?m+u?d(m) for all u belongs to U, m belongs to M and a belongs to Gamma, when U is a square closed Lie ideal of M.
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