Integral Closure of Powers of Generalized Edge Ideals

IF 0.4 4区 数学 Q4 MATHEMATICS Studia Scientiarum Mathematicarum Hungarica Pub Date : 2023-10-24 DOI:10.1556/012.2023.01543
Sirajul Haque
{"title":"Integral Closure of Powers of Generalized Edge Ideals","authors":"Sirajul Haque","doi":"10.1556/012.2023.01543","DOIUrl":null,"url":null,"abstract":"This article studies a new class of monomial ideals associated with a simple graph 𝐺, called generalized edge ideal, denoted by 𝐼 𝑔 (𝐺). Assuming that all the vertices 𝑥 have an exponent greater than 1 in 𝐼 𝑔 (𝐺), we completely characterize the graph 𝐺 for which 𝐼 𝑔 (𝐺) is integrally closed, and show that this is equivalent to 𝐼 𝑔 (𝐺) being normal i.e., all integral powers of 𝐼 𝑔 (𝐺) are integrally clased. We also give a necessary and sufficient condition for when 𝐺 is the star-shaped graph. Finally, we give a necessary and sufficient condition when the generalized edge ideal of a complete graph is integrally closed.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"67 1","pages":"0"},"PeriodicalIF":0.4000,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Scientiarum Mathematicarum Hungarica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1556/012.2023.01543","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

Abstract

This article studies a new class of monomial ideals associated with a simple graph 𝐺, called generalized edge ideal, denoted by 𝐼 𝑔 (𝐺). Assuming that all the vertices 𝑥 have an exponent greater than 1 in 𝐼 𝑔 (𝐺), we completely characterize the graph 𝐺 for which 𝐼 𝑔 (𝐺) is integrally closed, and show that this is equivalent to 𝐼 𝑔 (𝐺) being normal i.e., all integral powers of 𝐼 𝑔 (𝐺) are integrally clased. We also give a necessary and sufficient condition for when 𝐺 is the star-shaped graph. Finally, we give a necessary and sufficient condition when the generalized edge ideal of a complete graph is integrally closed.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
广义边理想幂的积分闭包
本文研究了与简单图𝐺相关的一类新的单项式理想,称为广义边理想,用𝐼𝑔(𝐺)表示。假设所有的顶点𝑥有指数大于1𝐼𝑔(𝐺),我们完全描述的图形𝐺𝐼𝑔(𝐺)完全关闭,并表明,这相当于𝐼𝑔(𝐺)正常即所有积分的权力𝐼𝑔(𝐺)整体一堂课。给出了𝐺为星形图的充分必要条件。最后给出了完全图的广义边理想是整闭的一个充分必要条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
1.30
自引率
0.00%
发文量
19
审稿时长
>12 weeks
期刊介绍: The journal publishes original research papers on various fields of mathematics, e.g., algebra, algebraic geometry, analysis, combinatorics, dynamical systems, geometry, mathematical logic, mathematical statistics, number theory, probability theory, set theory, statistical physics and topology.
期刊最新文献
Equalities for the 𝑟3-Crank of 3-Regular Overpartitions Convexity in (Colored) Affine Semigroups “Less” Strong Chromatic Indices and the (7, 4)-Conjecture The Endomorphism Conjecture for Graded Posets with Whitney Numbers at most 4 Refined Ehrhart Series and Bigraded Rings
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1