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.
Highlights
In this paper, we prove that if G is a Jordan u-generalized reverse derivation of a semi prime ring R of char.≠2, G is a u-generalized reverse derivation
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, D is uniquely determined by G and G must be a derivation
[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, 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 that G(x2) G(x)x xD(x), for all x in R
Summary
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, D is uniquely determined by G and G must be a derivation. JORDAN u-GENERALIZED REVERSE DERIVATIONS ON SEMIPRIME RINGS 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, G is a u-generalized reverse derivation. We show that if G is a Jordan u * generalized reverse derivation of a semi prime ring R of char.≠2, G is a u *generalized reverse derivation.
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