{"title":"交换弱调用-清洁群环","authors":"P. Danchev","doi":"10.15826/UMJ.2019.1.005","DOIUrl":null,"url":null,"abstract":"A ring \\(R\\) is called weakly invo-clean if any its element is the sum or the difference of an involution and an idempotent. For each commutative unital ring \\(R\\) and each abelian group \\(G\\), we find only in terms of \\(R\\), \\(G\\) and their sections a necessary and sufficient condition when the group ring \\(R[G]\\) is weakly invo-clean. Our established result parallels to that due to Danchev-McGovern published in J. Algebra (2015) and proved for weakly nil-clean rings.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Commutative Weakly Invo–Clean Group Rings\",\"authors\":\"P. Danchev\",\"doi\":\"10.15826/UMJ.2019.1.005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A ring \\\\(R\\\\) is called weakly invo-clean if any its element is the sum or the difference of an involution and an idempotent. For each commutative unital ring \\\\(R\\\\) and each abelian group \\\\(G\\\\), we find only in terms of \\\\(R\\\\), \\\\(G\\\\) and their sections a necessary and sufficient condition when the group ring \\\\(R[G]\\\\) is weakly invo-clean. Our established result parallels to that due to Danchev-McGovern published in J. Algebra (2015) and proved for weakly nil-clean rings.\",\"PeriodicalId\":36805,\"journal\":{\"name\":\"Ural Mathematical Journal\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ural Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15826/UMJ.2019.1.005\",\"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":"Ural Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15826/UMJ.2019.1.005","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
A ring \(R\) is called weakly invo-clean if any its element is the sum or the difference of an involution and an idempotent. For each commutative unital ring \(R\) and each abelian group \(G\), we find only in terms of \(R\), \(G\) and their sections a necessary and sufficient condition when the group ring \(R[G]\) is weakly invo-clean. Our established result parallels to that due to Danchev-McGovern published in J. Algebra (2015) and proved for weakly nil-clean rings.
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