{"title":"A Bezout ring with nonzero principal Jacobson radical","authors":"A. Gatalevych, A. Dmytruk","doi":"10.15330/cmp.14.1.72-75","DOIUrl":null,"url":null,"abstract":"In this paper, we study a commutative Bezout domain with nonzero Jacobson radical being a principal ideal. It has been proved that such a Bezout domain is a ring of the stable range 1. As a result, we have obtained that such a Bezout domain is a ring over which any matrix can be reduced to a canonical diagonal form by means of elementary transformations of its rows and columns.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Carpathian Mathematical Publications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15330/cmp.14.1.72-75","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study a commutative Bezout domain with nonzero Jacobson radical being a principal ideal. It has been proved that such a Bezout domain is a ring of the stable range 1. As a result, we have obtained that such a Bezout domain is a ring over which any matrix can be reduced to a canonical diagonal form by means of elementary transformations of its rows and columns.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
