Generalized derivations on prime near rings. (Q1950005)

Summary: Let \(N\) be a near ring. An additive mapping \(f\colon N\to N\) is said to be a right generalized (resp., left generalized) derivation with associated derivation \(d\) on \(N\) if \(f(xy)=f(x)y+xd(y)\) (resp., \(f(xy)=d(x)y+xf(y)\)) for all \(x,y\in N\). A mapping \(f\colon N\to N\) is said to be a generalized derivation with associated derivation \(d\) on \(N\) if \(f\) is both a right generalized and a left generalized derivation with associated derivation \(d\) on \(N\). The purpose of the present paper is to prove some theorems in the setting of a semigroup ideal of a 3-prime near ring admitting a generalized derivation, thereby extending some known results on derivations.