Generalized derivations and Left Ideals in Prime and Semiprime Rings
Let R be an associative ring, be the automorphisms of R, be a nonzero left ideal of R, F R R be a generalized derivation and d R Rbe an derivation. In the present paper we discuss the following situations: (i) F(xoy) a(xy yx) (ii) F([x; y] a(xy yx) (iii) d(x)od(y) a(xy yx) forall x; y 2 and a 2 f0; 1;oEUREUREUR1g. Also some related results have been obtained.