非零湮灭理想的全图的度规维数

IF 0.8 4区数学 Q2 MATHEMATICS

Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Pub Date : 2020-12-01 DOI:10.2478/auom-2020-0031

N. Abachi, S. Sahebi

{"title":"非零湮灭理想的全图的度规维数","authors":"N. Abachi, S. Sahebi","doi":"10.2478/auom-2020-0031","DOIUrl":null,"url":null,"abstract":"Abstract Let R be a commutative ring with identity which is not an integral domain. An ideal I of a ring R is called an annihilating ideal if there exists r ∈ R − {0} such that Ir = (0). Visweswaran and H. D. Patel associated a graph with the set of all non-zero annihilating ideals of R, denoted by Ω(R) as the graph with the vertex-set A(R)*, the set of all non-zero annihilating ideals of R and two distinct vertices I, J are joined if and only if I +J is also an annihilating ideal of R. In this paper, we study the metric dimension of Ω(R) and provide metric dimension formulas for Ω(R).","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":"3 1","pages":"5 - 14"},"PeriodicalIF":0.8000,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On the metric dimension of a total graph of non-zero annihilating ideals\",\"authors\":\"N. Abachi, S. Sahebi\",\"doi\":\"10.2478/auom-2020-0031\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Let R be a commutative ring with identity which is not an integral domain. An ideal I of a ring R is called an annihilating ideal if there exists r ∈ R − {0} such that Ir = (0). Visweswaran and H. D. Patel associated a graph with the set of all non-zero annihilating ideals of R, denoted by Ω(R) as the graph with the vertex-set A(R)*, the set of all non-zero annihilating ideals of R and two distinct vertices I, J are joined if and only if I +J is also an annihilating ideal of R. In this paper, we study the metric dimension of Ω(R) and provide metric dimension formulas for Ω(R).\",\"PeriodicalId\":55522,\"journal\":{\"name\":\"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica\",\"volume\":\"3 1\",\"pages\":\"5 - 14\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2020-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2478/auom-2020-0031\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2478/auom-2020-0031","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 3

摘要

摘要设R是一个非整域的恒等交换环。理想我叫做理想湮灭的环R是如果存在∈R−{0},Ir =(0)。Visweswaran和h·d·帕特尔相关图表的所有非零理想湮灭R,用Ω(R)作为图的顶点集(R) *,所有非零理想湮灭的R和两个不同的顶点,J加入当且仅当我+也是一个湮灭的理想R .摘要研究了Ω(R)的度量维数，给出了Ω(R)的度量维数公式。

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 the metric dimension of a total graph of non-zero annihilating ideals

Abstract Let R be a commutative ring with identity which is not an integral domain. An ideal I of a ring R is called an annihilating ideal if there exists r ∈ R − {0} such that Ir = (0). Visweswaran and H. D. Patel associated a graph with the set of all non-zero annihilating ideals of R, denoted by Ω(R) as the graph with the vertex-set A(R)*, the set of all non-zero annihilating ideals of R and two distinct vertices I, J are joined if and only if I +J is also an annihilating ideal of R. In this paper, we study the metric dimension of Ω(R) and provide metric dimension formulas for Ω(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

Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal is founded by Mirela Stefanescu and Silviu Sburlan in 1993 and is devoted to pure and applied mathematics. Published by Faculty of Mathematics and Computer Science, Ovidius University, Constanta, Romania.