Semigroup ideals and generalized semiderivations of prime near rings

Abstract

Let N be a near ring. An additive mapping F : N 􀀀! N is said to be a generalized semiderivation on N if there exists a semiderivation d : N 􀀀! N associated with a function g : N 􀀀! N such that F(xy) = F(x)y + g(x)d(y) = d(x)g(y) + xF(y) and F(g(x)) = g(F(x)) for all x; y 2 N. In this paper we prove some theorems in the setting of semigroup ideal of a 3-prime near ring admitting a nonzero generalized semiderivation associated with a nonzero semiderivation, thereby extending some known results on derivations, semiderivations and generalized derivations.