Codimension One Foliation and the Prime Spectrum of a Ring

IF 17.7 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-01-31 DOI:10.29020/nybg.ejpam.v17i1.4803

Badr Alharbi

引用次数: 0

Abstract

Let F be a transversally oriented codimension-one foliation of class Cr, r ≥ 0, on a closed manifold M. A leaf class of a leaf F is the union of all leaves having the same closure as F . Let X be the leaf classes space and X0 be the union of all open subsets of X homeomorphic to R or S1. In [2, Theorem 3.15] it is shown that if a codimension one foliation has a finite height, then the singular part of the space of leaf classes is homeomorphic to the prime spectrum (or simply the spectrum) of unitary commutative ring. In this paper we prove that the singular part of the space of leaf classes is homeomorphic to the spectrum of unitary commutative ring if and only if every family of totaly ordered leaves is bounded below.

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同维度一对折和环的质谱

让 F 是闭合流形 M 上类 Cr 的横向定向一维叶片，r ≥ 0。叶片 F 的叶类是与 F 具有相同闭合的所有叶片的联合。设 X 是叶类空间，X0 是 X 的所有同构于 R 或 S1 的开放子集的联合。在[2，定理 3.15]中证明，如果一个标度为一的叶子具有有限高，那么叶类空间的奇异部分与单元换元环的素谱（或简称谱）同构。在本文中，我们将证明当且仅当每一个全有序叶族都在下面有界时，叶类空间的奇异部分与单元交换环的谱是同构的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.