Abstract
In this paper, we prove commutativity of prime near rings by using the notion of β-derivations. Let M be a prime near ring. If there exist p,q ϵ M and two sided nonzero β-derivation f on M, where β:M→M is a homomorphism, satisfying the following conditions: f([s,t])=s^p [β(s),β(t)]s^q ∀ s,t ϵ M f([s,t])=-s^p [β(s),β(t)]s^q ∀ s,t ϵ M
Highlights
Throughout this paper M is a zero symmetric right near ring
We prove commutativity of prime near rings by using the notion of β-derivations
T ε M, sMt = 0, this implies that s = 0 or t = 0, M is called prime near ring (Bell and Mason, 1987)
Summary
Throughout this paper M is a zero symmetric right near ring. If M = {sεM ∶ 0s = 0} M is called zero symmetric. We prove commutativity of prime near rings by using the notion of β-derivations.
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