# On generalized derivations satisfying certain identities

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Let

*R*be a prime ring with char*R*≠ 2 and let*d*be a generalized derivation on*R*. We study the generalized derivation*d*satisfying any of the following identities:- (i)
*d*[(*x*,*y*)] = [*d*(*x*),*d*(*y*)] for all*x*,*y*∈*R*; - (ii)
*d*[(*x*,*y*)] = [*d*(*y*),*d*(*x*)] for all*x*,*y*∈*R*; - (iii)
either

*d*([*x*,*y*]) = [*d*(*x*),*d*(*y*)] or*d*([*x*,*y*]) = [*d*(*y*),*d*(*x*)] for all*x*,*y*∈*R*.

## Keywords

Prime Ring Generalize Derivation Proper Subgroup Quotient Ring Semiprime Ring
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