{"title":"积分域上$2\\times2$nil干净矩阵的刻画","authors":"K. N. Rajeswari, Umesh Gupta","doi":"10.13069/jacodesmath.451229","DOIUrl":null,"url":null,"abstract":"Let $R$ be any ring with identity. An element $a \\in R$ is called nil-clean, if $a=e+n$ where $e$ is an idempotent element and $n$ is a nil-potent element. In this paper we give necessary and sufficient conditions for a $2\\times 2$ matrix over an integral domain $R$ to be nil-clean.","PeriodicalId":37029,"journal":{"name":"Journal of Algebra Combinatorics Discrete Structures and Applications","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Characterization of $2\\\\times 2$ nil-clean matrices over integral domains\",\"authors\":\"K. N. Rajeswari, Umesh Gupta\",\"doi\":\"10.13069/jacodesmath.451229\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $R$ be any ring with identity. An element $a \\\\in R$ is called nil-clean, if $a=e+n$ where $e$ is an idempotent element and $n$ is a nil-potent element. In this paper we give necessary and sufficient conditions for a $2\\\\times 2$ matrix over an integral domain $R$ to be nil-clean.\",\"PeriodicalId\":37029,\"journal\":{\"name\":\"Journal of Algebra Combinatorics Discrete Structures and Applications\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-09-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra Combinatorics Discrete Structures and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.13069/jacodesmath.451229\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra Combinatorics Discrete Structures and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13069/jacodesmath.451229","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Characterization of $2\times 2$ nil-clean matrices over integral domains
Let $R$ be any ring with identity. An element $a \in R$ is called nil-clean, if $a=e+n$ where $e$ is an idempotent element and $n$ is a nil-potent element. In this paper we give necessary and sufficient conditions for a $2\times 2$ matrix over an integral domain $R$ to be nil-clean.
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