{"title":"The dual notion of $r$-submodules of modules","authors":"Faranak Farshadifar","doi":"10.24330/ieja.1299269","DOIUrl":null,"url":null,"abstract":"Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. \nA proper submodule $N$ of $M$ is said to be an $r$-submodule if \n$am\\in N$ with $(0:_Ma)=0$ implies that $m \\in N$ for each $a\\in R$ and $m\\in M$. \nThe purpose of this paper is to introduce and investigate the dual notion of $r$-submodules of $M$.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Electronic Journal of Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24330/ieja.1299269","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let $R$ be a commutative ring with identity and let $M$ be an $R$-module.
A proper submodule $N$ of $M$ is said to be an $r$-submodule if
$am\in N$ with $(0:_Ma)=0$ implies that $m \in N$ for each $a\in R$ and $m\in M$.
The purpose of this paper is to introduce and investigate the dual notion of $r$-submodules of $M$.
期刊介绍：
The International Electronic Journal of Algebra is published twice a year. IEJA is reviewed by Mathematical Reviews, MathSciNet, Zentralblatt MATH, Current Mathematical Publications. IEJA seeks previously unpublished papers that contain: Module theory Ring theory Group theory Algebras Comodules Corings Coalgebras Representation theory Number theory.
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