# GENERALIZED DERIVATIONS ON SEMIPRIME RINGS

• Published : 2011.11.30

#### Abstract

Let R be a prime ring, I a nonzero ideal of R and n a fixed positive integer. If R admits a generalized derivation F associated with a derivation d such that c for all x, $y{\in}I$. Then either R is commutative or n = 1, d = 0 and F is the identity map on R. Moreover in case R is a semiprime ring and $(F([x,\;y]))^n=[x,\;y]$ for all x, $y{\in}R$, then either R is commutative or n = 1, $d(R){\subseteq}Z(R)$, R contains a non-zero central ideal and for all $x{\in}R$.

#### Acknowledgement

Supported by : Natural Science Research Foundation

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