Jordan <i>u-</i>Generalized Reverse Derivations on Semiprime Rings

Abstract

ABSTRACT:In this paper, we prove that if G is a Jordan u-generalized reverse derivation of a semi prime ring R of char.≠2, then G is a u-generalized reverse derivation. Similarly, we show that if G is a Jordan u* generalized reverse derivation of a semi prime ring R of char.≠2, then G is a u*generalized reverse derivation. We also prove that the commutativity of R if G ([x,y]) =0. INTRODUCTION: M.Bresar [2] proved that for a semiprime ring R, if G is a function from R to R and D:RR is an additive mapping such that G(xy)G(x)yxD(y), for all x,yR,then D is uniquely determined by G and moreover G must be a derivation. In [1] Ashraf and Rehman proved that if R is a ring of char.≠2 such that R has a commutator which is not a zero divisor, then every Jordan generalized derivation on R is a generalized derivation.We know that an additive mapping G:RR is a Jordan generalized reverse derivation if there exists a derivation D from R to R such