整数多项式环的激进酉理想

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2025-12-01 Epub Date: 2025-11-19 DOI:10.1016/j.jpaa.2025.108134

Carmelo Antonio Finocchiaro , K. Alan Loper

{"title":"整数多项式环的激进酉理想","authors":"Carmelo Antonio Finocchiaro , K. Alan Loper","doi":"10.1016/j.jpaa.2025.108134","DOIUrl":null,"url":null,"abstract":"<div><div>Let <em>D</em> be a Dedekind domain (not a field) with finite residue fields and let <span><math><mi>Int</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span> be the ring of integer-valued polynomials over <em>D</em>. We completely classify in topological terms some relevant classes of radical unitary ideals of <span><math><mi>Int</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span> (and of its overrings). This project strongly extends the classification given in a previous paper and regarding special unitary ideals, precisely the ones lying over a given maximal ideal of <em>D</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108134"},"PeriodicalIF":0.7000,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On radical unitary ideals of rings of integer-valued polynomials\",\"authors\":\"Carmelo Antonio Finocchiaro , K. Alan Loper\",\"doi\":\"10.1016/j.jpaa.2025.108134\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Let <em>D</em> be a Dedekind domain (not a field) with finite residue fields and let <span><math><mi>Int</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span> be the ring of integer-valued polynomials over <em>D</em>. We completely classify in topological terms some relevant classes of radical unitary ideals of <span><math><mi>Int</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span> (and of its overrings). This project strongly extends the classification given in a previous paper and regarding special unitary ideals, precisely the ones lying over a given maximal ideal of <em>D</em>.</div></div>\",\"PeriodicalId\":54770,\"journal\":{\"name\":\"Journal of Pure and Applied Algebra\",\"volume\":\"229 12\",\"pages\":\"Article 108134\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Pure and Applied Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022404925002737\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/11/19 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pure and Applied Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404925002737","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/11/19 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

设D是一个有有限剩余域的Dedekind域（不是域），设Int(D)是D上的整值多项式环，我们用拓扑的方式完全分类了Int(D)（及其上环）的一些相关的根酉理想类。这个项目有力地扩展了前一篇文章中给出的分类，并且是关于特殊的幺正理想，即D的给定极大理想上的幺正理想。

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 radical unitary ideals of rings of integer-valued polynomials

Let D be a Dedekind domain (not a field) with finite residue fields and let

Int (D)

be the ring of integer-valued polynomials over D. We completely classify in topological terms some relevant classes of radical unitary ideals of

Int (D)

(and of its overrings). This project strongly extends the classification given in a previous paper and regarding special unitary ideals, precisely the ones lying over a given maximal ideal of D.

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

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

期刊介绍： The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.