Abstract
The main purpose of this paper is to show that zero symmetric prime near-rings, satisfying certain identities on n-derivations, are commutative rings.
Highlights
A near – ring is a set A together with two binary operations (+ and .) such that (i) (A,+) is a group,(ii) (A, .) is a semi group, and(iii) a,b,c εA; we have a.(b + c) = a.b + b.c .In this paper, A will be a zero symmetric near-ring ( i.e.,A satisfying 0.x = 0 x A) andC = {a ε A, ab = ba for all a ε A}
The main purpose of this paper is to show that zero symmetric prime near-rings, satisfying certain identities on n-derivations, are commutative rings
A is called a prime near-ring if aAb = { } which implies that either a = 0 or b = 0
Summary
Let N be a prime near-ring, U a nonzero semigroup right ideal Lemma 2.3.[3].Let N be a prime near-ring and U be a nonzero semigroup ideal of N. Lemma2.4.[2].Let N be a prime near-ring, d is n-derivation of N if and only if
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