{"title":"On φ-u-S-flat modules and nonnil-u-S-injective modules","authors":"Hwankoo Kim, Najib Mahdou, El Houssaine Oubouhou","doi":"10.1515/gmj-2023-2117","DOIUrl":null,"url":null,"abstract":"This paper introduces and studies the ϕ-u-<jats:italic>S</jats:italic>-flat (resp., nonnil-u-<jats:italic>S</jats:italic>-injective) modules, which are a generalization of both ϕ-flat modules and u-<jats:italic>S</jats:italic>-flat modules (resp., both nonnil-injective modules and u-<jats:italic>S</jats:italic>-injective modules). We give the Cartan–Eilenberg–Bass theorem for nonnil-u-<jats:italic>S</jats:italic>-Noetherian rings. Finally, we offer some new characterizations of the ϕ-von Neumann regular ring.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2023-2117","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
This paper introduces and studies the ϕ-u-S-flat (resp., nonnil-u-S-injective) modules, which are a generalization of both ϕ-flat modules and u-S-flat modules (resp., both nonnil-injective modules and u-S-injective modules). We give the Cartan–Eilenberg–Bass theorem for nonnil-u-S-Noetherian rings. Finally, we offer some new characterizations of the ϕ-von Neumann regular ring.
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