Turkish Journal of Mathematics
DOI

Abstract
In this paper, we introduce the notion of twosided \alphaderivation of a nearring and give some generalizations of [1]. Let N be a near ring. An additive mapping f: N\rightarrow N is called an { \it (\alpha, \beta)derivation } if there exist functions \alpha,\beta : N\rightarrow N such that f(xy)=f(x)\alpha(y)+\beta (x)f(y) for all x,y\in N. An additive mapping d:N\rightarrow N is called a twosided \alphaderivation if d is an (\alpha,1)derivation as well as a (1,\alpha)derivation. The purpose of this paper is to prove the following two assertions: (i) Let N be a semiprime nearring, I be a subset of N such that 0\in I, IN\subseteq I and d be a twosided \alphaderivation of N. If d acts as a homomorphism on I or as an antihomomorphism on I under certain conditions on \alpha, then d(I)= {0}. (ii) Let N be a prime nearring, I be a nonzero semigroup ideal of N, and d be a (\alpha, 1)derivation on N. If d+d is additive on I, then (N,+) is abelian.
Keywords
Prime nearring, semiprime nearring, (\alpha, 1)derivation, (1, \alpha)derivation, twosided \alphaderivation.
First Page
195
Last Page
204
Recommended Citation
ARGAÇ, NURCAN (2004) "On nearrings with twosided \alphaderivations," Turkish Journal of Mathematics: Vol. 28: No. 2, Article 10. Available at: https://journals.tubitak.gov.tr/math/vol28/iss2/10