伪评估域中的准二次模组

IF 0.6 3区 数学 Q3 MATHEMATICS
Masato Fujita, Masaru Kageyama
{"title":"伪评估域中的准二次模组","authors":"Masato Fujita, Masaru Kageyama","doi":"10.1007/s10998-024-00605-1","DOIUrl":null,"url":null,"abstract":"<p>We study quasi-quadratic modules in a pseudo-valuation domain <i>A</i> whose strict units admit a square root. Let <span>\\(\\mathfrak X_R^N\\)</span> denote the set of quasi-quadratic modules in an <i>R</i>-module <i>N</i>, where <i>R</i> is a commutative ring. It is known that there exists a unique overring <i>B</i> of <i>A</i> such that <i>B</i> is a valuation ring with the valuation group <span>\\((G,\\le )\\)</span> and the maximal ideal of <i>B</i> coincides with that of <i>A</i>. Let <i>F</i> be the residue field of <i>B</i>. In the above setting, we found a one-to-one correspondence between <span>\\({\\mathfrak {X}}_A^A\\)</span> and a subset of <span>\\(\\prod _{g \\in G,g \\ge e} {\\mathfrak {X}}_{F_0}^F\\)</span>.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"10 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quasi-quadratic modules in pseudo-valuation domain\",\"authors\":\"Masato Fujita, Masaru Kageyama\",\"doi\":\"10.1007/s10998-024-00605-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study quasi-quadratic modules in a pseudo-valuation domain <i>A</i> whose strict units admit a square root. Let <span>\\\\(\\\\mathfrak X_R^N\\\\)</span> denote the set of quasi-quadratic modules in an <i>R</i>-module <i>N</i>, where <i>R</i> is a commutative ring. It is known that there exists a unique overring <i>B</i> of <i>A</i> such that <i>B</i> is a valuation ring with the valuation group <span>\\\\((G,\\\\le )\\\\)</span> and the maximal ideal of <i>B</i> coincides with that of <i>A</i>. Let <i>F</i> be the residue field of <i>B</i>. In the above setting, we found a one-to-one correspondence between <span>\\\\({\\\\mathfrak {X}}_A^A\\\\)</span> and a subset of <span>\\\\(\\\\prod _{g \\\\in G,g \\\\ge e} {\\\\mathfrak {X}}_{F_0}^F\\\\)</span>.</p>\",\"PeriodicalId\":49706,\"journal\":{\"name\":\"Periodica Mathematica Hungarica\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-08-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Periodica Mathematica Hungarica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10998-024-00605-1\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Periodica Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10998-024-00605-1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

我们研究伪估值域 A 中的准二次模组,其严格单元允许有平方根。让 \(\mathfrak X_R^N\) 表示 R 模块 N 中准二次模组的集合,其中 R 是交换环。已知存在一个唯一的 A 的重环 B,使得 B 是一个具有估值群 \((G,\le )\) 的估值环,并且 B 的最大理想与 A 的最大理想重合。在上述设置中,我们找到了 \({\mathfrak {X}}_A^A\) 和 \(\prod _{g \in G,g \ge e} {\mathfrak {X}}_{F_0}^F\) 的子集之间的一一对应关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Quasi-quadratic modules in pseudo-valuation domain

Quasi-quadratic modules in pseudo-valuation domain

We study quasi-quadratic modules in a pseudo-valuation domain A whose strict units admit a square root. Let \(\mathfrak X_R^N\) denote the set of quasi-quadratic modules in an R-module N, where R is a commutative ring. It is known that there exists a unique overring B of A such that B is a valuation ring with the valuation group \((G,\le )\) and the maximal ideal of B coincides with that of A. Let F be the residue field of B. In the above setting, we found a one-to-one correspondence between \({\mathfrak {X}}_A^A\) and a subset of \(\prod _{g \in G,g \ge e} {\mathfrak {X}}_{F_0}^F\).

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
CiteScore
1.40
自引率
0.00%
发文量
67
审稿时长
>12 weeks
期刊介绍: Periodica Mathematica Hungarica is devoted to publishing research articles in all areas of pure and applied mathematics as well as theoretical computer science. To be published in the Periodica, a paper must be correct, new, and significant. Very strong submissions (upon the consent of the author) will be redirected to Acta Mathematica Hungarica. Periodica Mathematica Hungarica is the journal of the Hungarian Mathematical Society (János Bolyai Mathematical Society). The main profile of the journal is in pure mathematics, being open to applied mathematical papers with significant mathematical content.
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信