Two sided $\alpha $-derivations in 3-prime near-rings

Abstract

The purpose of this paper is to investigate two sided α-derivations satisfying certain differential identities on 3-prime near-rings. Some well-known results characterizing commutativity of 3-prime near-rings by derivations (semi-derivations) have been generalized. Furthermore, examples proving the necessity of the 3-primeness hypothesis are given. 2010 AMS Mathematics subject classification. Primary 16N60, 16W25, 16Y30. Keywords and phrases. 3-prime near-rings, two sided α-derivations, commutativity.

RESULTS IN PRIME RINGS WITH TWO SIDED α-DERIVATION Vol. 4(2) July. 2016, No. 4, pp. 38-45 LAHCEN TAOUFIQ AND ABDELKARIM BOUA

“…[7, Theorem 4] Let R be a prime ring. If d is a nonzero two sided α-derivation on R such that d(x • y) = x • y for all x, y ∈ R, then d = −α + Id R .…”