估值域的扩展与上升

IF 0.3 Q4 MATHEMATICS

Acta Mathematica Vietnamica Pub Date : 2021-11-13 DOI:10.1007/s40306-021-00461-y

Shai Sarussi

{"title":"估值域的扩展与上升","authors":"Shai Sarussi","doi":"10.1007/s40306-021-00461-y","DOIUrl":null,"url":null,"abstract":"<div>Suppose F is a field with valuation v and valuation domain Ov, E/F is a finite-dimensional field extension, and R is an Ov-subalgebra of E such that F ⋅ R = E and R ∩ F = Ov. It is known that R satisfies LO, INC, GD and SGB over Ov; it is also known that under certain conditions R satisfies GU over Ov. In this paper, we present a necessary and sufficient condition for the existence of such R that does not satisfy GU over Ov. We also present an explicit example of such R that does not satisfy GU over Ov.</div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"47 3","pages":"683 - 687"},"PeriodicalIF":0.3000,"publicationDate":"2021-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Extensions of Valuation Domains and Going-up\",\"authors\":\"Shai Sarussi\",\"doi\":\"10.1007/s40306-021-00461-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>Suppose F is a field with valuation v and valuation domain Ov, E/F is a finite-dimensional field extension, and R is an Ov-subalgebra of E such that F ⋅ R = E and R ∩ F = Ov. It is known that R satisfies LO, INC, GD and SGB over Ov; it is also known that under certain conditions R satisfies GU over Ov. In this paper, we present a necessary and sufficient condition for the existence of such R that does not satisfy GU over Ov. We also present an explicit example of such R that does not satisfy GU over Ov.</div>\",\"PeriodicalId\":45527,\"journal\":{\"name\":\"Acta Mathematica Vietnamica\",\"volume\":\"47 3\",\"pages\":\"683 - 687\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-11-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Vietnamica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40306-021-00461-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Vietnamica","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40306-021-00461-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

假设F是一个具有赋值v和赋值域Ov的域，E/F是有限维域的扩张，R是E的Ov子代数，使得F·R=E和R≠F=Ov。已知R在Ov上满足LO、INC、GD和SGB；还已知在某些条件下R在Ov上满足GU。本文给出了在Ov上不满足GU的R存在的一个充要条件。我们还给出了一个这样的R的显式例子，它在Ov上不满足GU。

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

Extensions of Valuation Domains and Going-up

Suppose F is a field with valuation v and valuation domain O_v, E/F is a finite-dimensional field extension, and R is an O_v-subalgebra of E such that F ⋅ R = E and R ∩ F = O_v. It is known that R satisfies LO, INC, GD and SGB over O_v; it is also known that under certain conditions R satisfies GU over O_v. In this paper, we present a necessary and sufficient condition for the existence of such R that does not satisfy GU over O_v. We also present an explicit example of such R that does not satisfy GU over O_v.

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

Acta Mathematica Vietnamica MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.