{"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}
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 $varphi (R)$.
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