A NOTE ON β-DERIVATIONS IN PRIME NEAR RING

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...

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Bibliographic Details
Published in:Matrix science mathematic (Online) 2021-07, Vol.5 (1), p.20-23
Main Authors: Khan, Abdul Rauf, Mumtaz, Khadija, Waqas, Muhammad Mohsin
Format: Article
Language:English
Subjects:
commutativity
homomorphism
β-derivations
Online Access:Get full text
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Summary: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
ISSN:2521-0831
2521-084X
DOI:10.26480/msmk.01.2021.20.23