{"title":"弱拟invo清洁环","authors":"F. Rashedi","doi":"10.56415/qrs.v31.08","DOIUrl":null,"url":null,"abstract":"We introduce the notion of weakly quasi invo-clean rings where every element $ r $ can be written as $ r=v+e $ or $ r=v-e $, where $v\\in Qinv(R)$ and $ e\\in Id(R) $. We study various properties of weakly quasi invo-clean elements and weakly quasi invo-clean rings. We prove that the ring $ R=\\prod_{i\\in I} R_i $, where all rings $ R_i $ are weakly quasi invo-clean, is weakly quasi invo-clean ring if and only if all factors but one are quasi invo-clean.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weakly quasi invo-clean rings\",\"authors\":\"F. Rashedi\",\"doi\":\"10.56415/qrs.v31.08\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce the notion of weakly quasi invo-clean rings where every element $ r $ can be written as $ r=v+e $ or $ r=v-e $, where $v\\\\in Qinv(R)$ and $ e\\\\in Id(R) $. We study various properties of weakly quasi invo-clean elements and weakly quasi invo-clean rings. We prove that the ring $ R=\\\\prod_{i\\\\in I} R_i $, where all rings $ R_i $ are weakly quasi invo-clean, is weakly quasi invo-clean ring if and only if all factors but one are quasi invo-clean.\",\"PeriodicalId\":38681,\"journal\":{\"name\":\"Quasigroups and Related Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quasigroups and Related Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.56415/qrs.v31.08\",\"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":"Quasigroups and Related Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56415/qrs.v31.08","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
We introduce the notion of weakly quasi invo-clean rings where every element $ r $ can be written as $ r=v+e $ or $ r=v-e $, where $v\in Qinv(R)$ and $ e\in Id(R) $. We study various properties of weakly quasi invo-clean elements and weakly quasi invo-clean rings. We prove that the ring $ R=\prod_{i\in I} R_i $, where all rings $ R_i $ are weakly quasi invo-clean, is weakly quasi invo-clean ring if and only if all factors but one are quasi invo-clean.