{"title":"不可逆元素唯一干净的环","authors":"Y. Guo, H. Jiang","doi":"10.31926/but.mif.2023.3.65.1.12","DOIUrl":null,"url":null,"abstract":"We call a ring R a generalized uniquely clean (or GUC for short) if every not invertible element in R is uniquely clean. Let R be a ring. It is shown that R is GUC if and only if it is a local ring or a uniquely clean ring. Thus the GUC ring is a generalization of the local ring. Some basic properties of GUC rings are proved.","PeriodicalId":53266,"journal":{"name":"Bulletin of the Transilvania University of Brasov Series V Economic Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rings in which not invertible elements are uniquely clean\",\"authors\":\"Y. Guo, H. Jiang\",\"doi\":\"10.31926/but.mif.2023.3.65.1.12\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We call a ring R a generalized uniquely clean (or GUC for short) if every not invertible element in R is uniquely clean. Let R be a ring. It is shown that R is GUC if and only if it is a local ring or a uniquely clean ring. Thus the GUC ring is a generalization of the local ring. Some basic properties of GUC rings are proved.\",\"PeriodicalId\":53266,\"journal\":{\"name\":\"Bulletin of the Transilvania University of Brasov Series V Economic Sciences\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Transilvania University of Brasov Series V Economic Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31926/but.mif.2023.3.65.1.12\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Transilvania University of Brasov Series V Economic Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31926/but.mif.2023.3.65.1.12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Rings in which not invertible elements are uniquely clean
We call a ring R a generalized uniquely clean (or GUC for short) if every not invertible element in R is uniquely clean. Let R be a ring. It is shown that R is GUC if and only if it is a local ring or a uniquely clean ring. Thus the GUC ring is a generalization of the local ring. Some basic properties of GUC rings are proved.
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