• (1,α)- DERIVATIONS IN Γ- NEAR RING

Abstract

In this paper, we introduce the notion of - derivation of  near ring and give some generalizations of [1]. The purpose of this paper is to prove the following two assertions: (i) Let Mbe a semiprime  near ring, U  be a subset of M such that 0  and  be a -derivation of M. If  acts as homomorphism on U or as antihomomorphism on U under certain conditions on then .  (ii) Let M be a prime  near ring, U be a nonzero semigroup ideal of M, and  be a derivation on M. If  for all  then  is abelian.