{"title":"关于φ-u-S平模块和非零-u-S注入模块","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":"{\"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}","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}
On φ-u-S-flat modules and nonnil-u-S-injective modules
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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