本质上是等伸缩模块和环

IF 1 Q1 MATHEMATICS

Carpathian Mathematical Publications Pub Date : 2022-04-27 DOI:10.15330/cmp.14.1.76-85

A. K. Chaturvedi, S. Kumar, S. Prakash, N. Kumar

{"title":"本质上是等伸缩模块和环","authors":"A. K. Chaturvedi, S. Kumar, S. Prakash, N. Kumar","doi":"10.15330/cmp.14.1.76-85","DOIUrl":null,"url":null,"abstract":"A.K. Chaturvedi et al. (2021) call a module $M$ essentially iso-retractable if for every essential submodule $N$ of $M$ there exists an isomorphism $f : M\\rightarrow N.$ We characterize essentially iso-retractable modules, co-semisimple modules ($V$-rings), principal right ideal domains, simple modules and semisimple modules. Over a Noetherian ring, we prove that every essentially iso-retractable module is isomorphic to a direct sum of uniform submodules.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Essentially iso-retractable modules and rings\",\"authors\":\"A. K. Chaturvedi, S. Kumar, S. Prakash, N. Kumar\",\"doi\":\"10.15330/cmp.14.1.76-85\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A.K. Chaturvedi et al. (2021) call a module $M$ essentially iso-retractable if for every essential submodule $N$ of $M$ there exists an isomorphism $f : M\\\\rightarrow N.$ We characterize essentially iso-retractable modules, co-semisimple modules ($V$-rings), principal right ideal domains, simple modules and semisimple modules. Over a Noetherian ring, we prove that every essentially iso-retractable module is isomorphic to a direct sum of uniform submodules.\",\"PeriodicalId\":42912,\"journal\":{\"name\":\"Carpathian Mathematical Publications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2022-04-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Carpathian Mathematical Publications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15330/cmp.14.1.76-85\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Carpathian Mathematical Publications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15330/cmp.14.1.76-85","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

A.K. Chaturvedi等人(2021)称模$M$本质等可伸缩，如果对于$M$的每个基本子模$N$存在同构$f: M\右列N$。我们描述了本质等可伸缩模、协半单模($V$-环)、主右理想域、简单模和半单模。在一个noether环上，我们证明了每一个本质上等可伸缩的模都同构于一致子模的直和。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Essentially iso-retractable modules and rings

A.K. Chaturvedi et al. (2021) call a module $M$ essentially iso-retractable if for every essential submodule $N$ of $M$ there exists an isomorphism $f : M\rightarrow N.$ We characterize essentially iso-retractable modules, co-semisimple modules ($V$-rings), principal right ideal domains, simple modules and semisimple modules. Over a Noetherian ring, we prove that every essentially iso-retractable module is isomorphic to a direct sum of uniform submodules.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Carpathian Mathematical Publications MATHEMATICS-

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

25 weeks