曲线奇点的迹理想集合

IF 0.8 2区数学 Q2 MATHEMATICS

Israel Journal of Mathematics Pub Date : 2024-09-03 DOI:10.1007/s11856-024-2661-6

Toshinori Kobayashi, Shinya Kumashiro

{"title":"曲线奇点的迹理想集合","authors":"Toshinori Kobayashi, Shinya Kumashiro","doi":"10.1007/s11856-024-2661-6","DOIUrl":null,"url":null,"abstract":"<p>We investigate a problem of when commutative local domains have a finite number of trace ideals. The problem is left for the case of dimension one. In this paper, with a necessary assumption, we give a complete answer by using integrally closed ideals. We also explore properties of such domains related to birational extensions, reflexive ideals, and reflexive Ulrich modules. Special attention is given in the case of numerical semigroup rings of non-gap four. We then obtain a criterion for a ring to have a finite number of reflexive ideals up to isomorphism. Non-domains arising from fiber products are also explored.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":"39 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The set of trace ideals of curve singularities\",\"authors\":\"Toshinori Kobayashi, Shinya Kumashiro\",\"doi\":\"10.1007/s11856-024-2661-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We investigate a problem of when commutative local domains have a finite number of trace ideals. The problem is left for the case of dimension one. In this paper, with a necessary assumption, we give a complete answer by using integrally closed ideals. We also explore properties of such domains related to birational extensions, reflexive ideals, and reflexive Ulrich modules. Special attention is given in the case of numerical semigroup rings of non-gap four. We then obtain a criterion for a ring to have a finite number of reflexive ideals up to isomorphism. Non-domains arising from fiber products are also explored.</p>\",\"PeriodicalId\":14661,\"journal\":{\"name\":\"Israel Journal of Mathematics\",\"volume\":\"39 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Israel Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11856-024-2661-6\",\"RegionNum\":2,\"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":"Israel Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11856-024-2661-6","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了交换局部域何时具有有限数量的痕理想的问题。这个问题留待维数为一的情况下解决。在本文中，通过一个必要的假设，我们利用整闭理想给出了一个完整的答案。我们还探讨了此类域与双向扩展、反身理想和反身乌尔里希模块相关的性质。我们特别关注了非间隙四的数值半群环的情况。然后，我们得到了一个标准，即一个环具有有限数量的同构反折理想。我们还探讨了由纤维积产生的非域。

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

The set of trace ideals of curve singularities

We investigate a problem of when commutative local domains have a finite number of trace ideals. The problem is left for the case of dimension one. In this paper, with a necessary assumption, we give a complete answer by using integrally closed ideals. We also explore properties of such domains related to birational extensions, reflexive ideals, and reflexive Ulrich modules. Special attention is given in the case of numerical semigroup rings of non-gap four. We then obtain a criterion for a ring to have a finite number of reflexive ideals up to isomorphism. Non-domains arising from fiber products are also explored.

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

Israel Journal of Mathematics 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.