关于所有子模块都有唯一闭包的模块的一些注意事项

IF 0.9 4区数学 Q1 Mathematics Miskolc Mathematical Notes Pub Date : 2022-01-01 DOI:10.18514/mmn.2022.3876

Özgür Taşdemir

{"title":"关于所有子模块都有唯一闭包的模块的一些注意事项","authors":"Özgür Taşdemir","doi":"10.18514/mmn.2022.3876","DOIUrl":null,"url":null,"abstract":"A module M is called a UC-module if whenever every submodule of M has a unique closure. In this paper, we establish new characterizations of several well-studied classes of rings in terms of UC-modules, and show that UC is not a Morita invariant property. In addition, we study the behaviour of UC-modules under excellent extensions of rings.","PeriodicalId":49806,"journal":{"name":"Miskolc Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some notes on modules in which all submodules have a unique closure\",\"authors\":\"Özgür Taşdemir\",\"doi\":\"10.18514/mmn.2022.3876\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A module M is called a UC-module if whenever every submodule of M has a unique closure. In this paper, we establish new characterizations of several well-studied classes of rings in terms of UC-modules, and show that UC is not a Morita invariant property. In addition, we study the behaviour of UC-modules under excellent extensions of rings.\",\"PeriodicalId\":49806,\"journal\":{\"name\":\"Miskolc Mathematical Notes\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Miskolc Mathematical Notes\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.18514/mmn.2022.3876\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Miskolc Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.18514/mmn.2022.3876","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

如果模块M的每个子模块都有一个唯一的闭包，则模块M称为uc模块。在本文中，我们用UC-模建立了一些已经被广泛研究的环类的新的刻画，并证明了UC不是Morita不变性质。此外，我们还研究了环的优秀扩展下uc模的行为。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Some notes on modules in which all submodules have a unique closure

A module M is called a UC-module if whenever every submodule of M has a unique closure. In this paper, we establish new characterizations of several well-studied classes of rings in terms of UC-modules, and show that UC is not a Morita invariant property. In addition, we study the behaviour of UC-modules under excellent extensions of rings.

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

Miskolc Mathematical Notes Mathematics-Algebra and Number Theory

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： Miskolc Mathematical Notes, HU ISSN 1787-2405 (printed version), HU ISSN 1787-2413 (electronic version), is a peer-reviewed international mathematical journal aiming at the dissemination of results in many fields of pure and applied mathematics.

期刊最新文献

A modified nonmonotone filter QP-free method Answers to George-Radenovic-Reshma-Shukla questions in rectangular b-metric spaces Fixed point theorems for upper semicontinuous multivalued operators in locally convex spaces Cayley line graphs of transitive groupoids Ostrowski type inequalities for functions of two variables via generalized fractional integrals