交换环上与模相关的湮灭图

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2022-04-30 DOI:10.1142/s1005386722000232

R. Raja, S. Pirzada

{"title":"交换环上与模相关的湮灭图","authors":"R. Raja, S. Pirzada","doi":"10.1142/s1005386722000232","DOIUrl":null,"url":null,"abstract":"Let [Formula: see text] be a commutative ring with unity, [Formula: see text] be a unitary [Formula: see text]-module and [Formula: see text] be a simple connected graph. We examine different equivalence relations on subsets [Formula: see text], [Formula: see text] and [Formula: see text] of [Formula: see text], where [Formula: see text] is the set of full-annihilators, [Formula: see text] is the set of semi-annihilators and [Formula: see text] is the set of star-annihilators in [Formula: see text]. We prove that elements [Formula: see text] are neighborhood similar in the annihilating graph [Formula: see text] if and only if the submodules [Formula: see text] and [Formula: see text] of [Formula: see text] are equal. We study the isomorphism of annihilating graphs arising from [Formula: see text] and the tensor product [Formula: see text], where [Formula: see text], [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On Annihilating Graphs Associated with Modules over Commutative Rings\",\"authors\":\"R. Raja, S. Pirzada\",\"doi\":\"10.1142/s1005386722000232\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let [Formula: see text] be a commutative ring with unity, [Formula: see text] be a unitary [Formula: see text]-module and [Formula: see text] be a simple connected graph. We examine different equivalence relations on subsets [Formula: see text], [Formula: see text] and [Formula: see text] of [Formula: see text], where [Formula: see text] is the set of full-annihilators, [Formula: see text] is the set of semi-annihilators and [Formula: see text] is the set of star-annihilators in [Formula: see text]. We prove that elements [Formula: see text] are neighborhood similar in the annihilating graph [Formula: see text] if and only if the submodules [Formula: see text] and [Formula: see text] of [Formula: see text] are equal. We study the isomorphism of annihilating graphs arising from [Formula: see text] and the tensor product [Formula: see text], where [Formula: see text], [Formula: see text].\",\"PeriodicalId\":50958,\"journal\":{\"name\":\"Algebra Colloquium\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra Colloquium\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1005386722000232\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra Colloquium","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1005386722000232","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 3

摘要

设[公式:见文]是一个具有单位的交换环，[公式:见文]是一个酉[公式:见文]-模，[公式:见文]是一个简单连通图。我们研究了[公式:见文]的子集[公式:见文]、[公式:见文]和[公式:见文]上的不同等价关系，其中[公式:见文]是完全湮灭子的集合，[公式:见文]是半湮灭子的集合，[公式:见文]是[公式:见文]中的星湮灭子的集合。证明元素[公式:见文]在湮灭图[公式:见文]中邻域相似当且仅当[公式:见文]的子模[公式:见文]和[公式:见文]相等。我们研究由[公式:见文]和张量积[公式:见文]引起的湮灭图的同构，其中[公式:见文]，[公式:见文]。

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

On Annihilating Graphs Associated with Modules over Commutative Rings

Let [Formula: see text] be a commutative ring with unity, [Formula: see text] be a unitary [Formula: see text]-module and [Formula: see text] be a simple connected graph. We examine different equivalence relations on subsets [Formula: see text], [Formula: see text] and [Formula: see text] of [Formula: see text], where [Formula: see text] is the set of full-annihilators, [Formula: see text] is the set of semi-annihilators and [Formula: see text] is the set of star-annihilators in [Formula: see text]. We prove that elements [Formula: see text] are neighborhood similar in the annihilating graph [Formula: see text] if and only if the submodules [Formula: see text] and [Formula: see text] of [Formula: see text] are equal. We study the isomorphism of annihilating graphs arising from [Formula: see text] and the tensor product [Formula: see text], where [Formula: see text], [Formula: see text].

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

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.