图团数小于5的有限环

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2021-09-01 DOI:10.1142/S1005386721000419

Qiong Liu, Tongsuo Wu, Jin Guo

{"title":"图团数小于5的有限环","authors":"Qiong Liu, Tongsuo Wu, Jin Guo","doi":"10.1142/S1005386721000419","DOIUrl":null,"url":null,"abstract":"Let [Formula: see text] be a commutative ring and [Formula: see text] be its zero-divisor graph. We completely determine the structure of all finite commutative rings whose zero-divisor graphs have clique number one, two, or three. Furthermore, if [Formula: see text] (each [Formula: see text] is local for [Formula: see text]), we also give algebraic characterizations of the ring [Formula: see text] when the clique number of [Formula: see text] is four.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":"11 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Finite Rings Whose Graphs Have Clique Number Less than Five\",\"authors\":\"Qiong Liu, Tongsuo Wu, Jin Guo\",\"doi\":\"10.1142/S1005386721000419\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let [Formula: see text] be a commutative ring and [Formula: see text] be its zero-divisor graph. We completely determine the structure of all finite commutative rings whose zero-divisor graphs have clique number one, two, or three. Furthermore, if [Formula: see text] (each [Formula: see text] is local for [Formula: see text]), we also give algebraic characterizations of the ring [Formula: see text] when the clique number of [Formula: see text] is four.\",\"PeriodicalId\":50958,\"journal\":{\"name\":\"Algebra Colloquium\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra Colloquium\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/S1005386721000419\",\"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/S1005386721000419","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: 0

摘要

设[公式:见文]是一个交换环，[公式:见文]是它的零因子图。我们完全确定了所有有限交换环的结构，其零因子图具有团数1、2或3。进一步，如果[公式:见文](每个[公式:见文]都是[公式:见文]的局部)，我们也给出了当[公式:见文]的团数为4时环[公式:见文]的代数刻画。

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

Finite Rings Whose Graphs Have Clique Number Less than Five

Let [Formula: see text] be a commutative ring and [Formula: see text] be its zero-divisor graph. We completely determine the structure of all finite commutative rings whose zero-divisor graphs have clique number one, two, or three. Furthermore, if [Formula: see text] (each [Formula: see text] is local for [Formula: see text]), we also give algebraic characterizations of the ring [Formula: see text] when the clique number of [Formula: see text] is four.

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.