STRUCTURE OF A RING IN WHICH EVERY ELEMENT IS SUM OF 3, 4 OR 5 COMMUTING TRIPOTENTS

Kumar Napoleon, Deka, Helen K. Saikia
{"title":"STRUCTURE OF A RING IN WHICH EVERY ELEMENT IS SUM OF 3, 4 OR 5 COMMUTING TRIPOTENTS","authors":"Kumar Napoleon, Deka, Helen K. Saikia","doi":"10.37418/amsj.12.11.4","DOIUrl":null,"url":null,"abstract":"In this paper we show if $R$ be a ring in which every element is sum of three commuting tripotents then for every $k\\in R$ we have $(k-3)(k-2)^2(k-1)^2k^2(k+1)^2(k+2)^2(k+3)=0$, if every element of $R$ is sum of four commuting tripotents then for every $k\\in R$ we have $(k-4)(k-3)(k-2)^2(k-1)^2k^4(k+1)^2(k+2)^2(k+3)(k+4)=0$, if every element of $R$ is sum of five commuting tripotents then for every $k\\in R$ we have $(k-5)(k-4)(k-3)^2(k-2)^3(k-1)^3k^4(k+1)^3(k+2)^3(k+3)^2(k+4)(k+5)=0$. Then we discuss the properties of these type of ring. Finally we find the general structure of a ring in which every element is sum of $n$ commuting tripotents and discuss the properties of it.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"24 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics: Scientific Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37418/amsj.12.11.4","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 show if $R$ be a ring in which every element is sum of three commuting tripotents then for every $k\in R$ we have $(k-3)(k-2)^2(k-1)^2k^2(k+1)^2(k+2)^2(k+3)=0$, if every element of $R$ is sum of four commuting tripotents then for every $k\in R$ we have $(k-4)(k-3)(k-2)^2(k-1)^2k^4(k+1)^2(k+2)^2(k+3)(k+4)=0$, if every element of $R$ is sum of five commuting tripotents then for every $k\in R$ we have $(k-5)(k-4)(k-3)^2(k-2)^3(k-1)^3k^4(k+1)^3(k+2)^3(k+3)^2(k+4)(k+5)=0$. Then we discuss the properties of these type of ring. Finally we find the general structure of a ring in which every element is sum of $n$ commuting tripotents and discuss the properties of it.
环结构,其中每个元素都是 3、4 或 5 个交换三等分元素之和
在本文中,我们证明如果 $R$ 是一个环,其中每个元素都是三个交换三元组之和,那么对于 R$ 中的每个 $k\ 都有 $(k-3)(k-2)^2(k-1)^2k^2(k+1)^2(k+2)^2(k+3)=0$、如果 $R$ 中的每个元素都是四个交换三等分的和,那么对于 R$ 中的每个 $k\ 都有 $(k-4)(k-3)(k-2)^2(k-1)^2k^4(k+1)^2(k+2)^2(k+3)(k+4)=0$、如果 $R$ 中的每个元素都是五个相交的三等分之和,那么对于 R$ 中的每个 $k\ 都有 $(k-5)(k-4)(k-3)^2(k-2)^3(k-1)^3k^4(k+1)^3(k+2)^3(k+3)^2(k+4)(k+5)=0$。然后,我们讨论这类环的性质。最后,我们将找到每个元素都是 $n$ 换向三等分之和的环的一般结构,并讨论它的性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信