Abdul Rauf Khan, Khadija Mumtaz, Muhammad Mohsin Waqas
{"title":"A NOTE ON β-DERIVATIONS IN PRIME NEAR RING","authors":"Abdul Rauf Khan, Khadija Mumtaz, Muhammad Mohsin Waqas","doi":"10.26480/msmk.01.2021.20.23","DOIUrl":null,"url":null,"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","PeriodicalId":32521,"journal":{"name":"Matrix Science Mathematic","volume":"47 62","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Matrix Science Mathematic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26480/msmk.01.2021.20.23","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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
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