Abdul Rauf Khan, Khadija Mumtaz, Muhammad Mohsin Waqas
{"title":"关于素近环的交换性","authors":"Abdul Rauf Khan, Khadija Mumtaz, Muhammad Mohsin Waqas","doi":"10.26480/msmk.01.2021.06.15","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 zero symmetric prime near ring. If there exist p ≥ 0, q ≥ 0 and a nonzero two sided β-derivation d on M, where β : M → M is a homomorphism, such that d satisfy one of the following conditions: [β(s),d(t)] = sp(β(s)oβ(t))sq ∀ s, t ∈ M [β(s),d(t)] = −sp(β(s)oβ(t))sq ∀ s, t ∈ M [d(s),β(t)] = tp(β(s)oβ(t))tq ∀ s, t ∈ M [d(s),β(t)] = −tp(β(s)oβ(t)tq ∀ s, t ∈ M","PeriodicalId":32521,"journal":{"name":"Matrix Science Mathematic","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON COMMUTATIVITY OF PRIME NEAR RINGS\",\"authors\":\"Abdul Rauf Khan, Khadija Mumtaz, Muhammad Mohsin Waqas\",\"doi\":\"10.26480/msmk.01.2021.06.15\",\"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 zero symmetric prime near ring. If there exist p ≥ 0, q ≥ 0 and a nonzero two sided β-derivation d on M, where β : M → M is a homomorphism, such that d satisfy one of the following conditions: [β(s),d(t)] = sp(β(s)oβ(t))sq ∀ s, t ∈ M [β(s),d(t)] = −sp(β(s)oβ(t))sq ∀ s, t ∈ M [d(s),β(t)] = tp(β(s)oβ(t))tq ∀ s, t ∈ M [d(s),β(t)] = −tp(β(s)oβ(t)tq ∀ s, t ∈ M\",\"PeriodicalId\":32521,\"journal\":{\"name\":\"Matrix Science Mathematic\",\"volume\":\" \",\"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.01.2021.06.15\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Matrix Science Mathematic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26480/msmk.01.2021.06.15","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we prove commutativity of prime near rings by using the notion of β-derivations. Let M be a zero symmetric prime near ring. If there exist p ≥ 0, q ≥ 0 and a nonzero two sided β-derivation d on M, where β : M → M is a homomorphism, such that d satisfy one of the following conditions: [β(s),d(t)] = sp(β(s)oβ(t))sq ∀ s, t ∈ M [β(s),d(t)] = −sp(β(s)oβ(t))sq ∀ s, t ∈ M [d(s),β(t)] = tp(β(s)oβ(t))tq ∀ s, t ∈ M [d(s),β(t)] = −tp(β(s)oβ(t)tq ∀ s, t ∈ M
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
