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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

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 𝑢1 , 𝑣1 𝜖 𝑀 and two sided generalized β-derivation G associated with the nonzero two sided β-derivation 𝑔 on M, where 𝛽: 𝑀 → 𝑀 is a homomorphism, satisfying the following conditions: i. 𝐺([𝑝1 , 𝑞1 ]) = 𝑝1 𝑢1[𝛽(𝑝1 ),𝛽(𝑞1 )]𝑝1 𝑣1 ∀ 𝑝1 , 𝑞1 𝜖 𝑀 ii. 𝐺([𝑝1 , 𝑞1 ]) = 𝑝1 𝑢1[𝛽(𝑝1 ),𝛽(𝑞1 )]𝑝1 𝑣1 ∀ 𝑝1 , 𝑞1 𝜖 𝑀 Then M is a commutative ring