交换环的共模理想图的一些性质

IF 0.6 Q3 MATHEMATICS Transactions on Combinatorics Pub Date : 2017-03-01 DOI:10.22108/TOC.2017.20429

Z. Jafari, M. Azadi

{"title":"交换环的共模理想图的一些性质","authors":"Z. Jafari, M. Azadi","doi":"10.22108/TOC.2017.20429","DOIUrl":null,"url":null,"abstract":"Let $R$ be a commutative ring with identity‎. ‎We use‎ ‎$varphi (R)$ to denote the comaximal ideal graph‎. ‎The vertices‎ ‎of $varphi (R)$ are proper ideals of R which are not contained‎ ‎in the Jacobson radical of $R$‎, ‎and two vertices $I$ and $J$ are‎ ‎adjacent if and only if $I‎ + ‎J = R$‎. ‎In this paper we show some‎ ‎properties of this graph together with planarity of line graph‎ ‎associated to $varphi (R)$‎.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"6 1","pages":"29-37"},"PeriodicalIF":0.6000,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Some properties of comaximal ideal graph of a commutative ring\",\"authors\":\"Z. Jafari, M. Azadi\",\"doi\":\"10.22108/TOC.2017.20429\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $R$ be a commutative ring with identity‎. ‎We use‎ ‎$varphi (R)$ to denote the comaximal ideal graph‎. ‎The vertices‎ ‎of $varphi (R)$ are proper ideals of R which are not contained‎ ‎in the Jacobson radical of $R$‎, ‎and two vertices $I$ and $J$ are‎ ‎adjacent if and only if $I‎ + ‎J = R$‎. ‎In this paper we show some‎ ‎properties of this graph together with planarity of line graph‎ ‎associated to $varphi (R)$‎.\",\"PeriodicalId\":43837,\"journal\":{\"name\":\"Transactions on Combinatorics\",\"volume\":\"6 1\",\"pages\":\"29-37\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2017-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions on Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22108/TOC.2017.20429\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions on Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/TOC.2017.20429","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: 1

摘要

设$R$是具有恒等式的交换环‎. ‎我们使用‎ ‎$varphi（R）$表示共模理想图‎. ‎顶点‎ ‎$varphi（R）$是R的不包含的适当理想‎ ‎在$R的Jacobson偏旁$‎, ‎并且两个顶点$I$和$J$是‎ ‎相邻当且仅当$I‎ + ‎J=R$‎. ‎在这篇论文中，我们展示了‎ ‎该图的性质与线图的平面性‎ ‎与$varphi（R）关联$‎.

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 properties of comaximal ideal graph of a commutative ring

Let $R$ be a commutative ring with identity‎. ‎We use‎ ‎$varphi (R)$ to denote the comaximal ideal graph‎. ‎The vertices‎ ‎of $varphi (R)$ are proper ideals of R which are not contained‎ ‎in the Jacobson radical of $R$‎, ‎and two vertices $I$ and $J$ are‎ ‎adjacent if and only if $I‎ + ‎J = R$‎. ‎In this paper we show some‎ ‎properties of this graph together with planarity of line graph‎ ‎associated to $varphi (R)$‎.

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