论Nagata关于高度一个极大理想和深度一个极小素理想的结果(一)

Q4 Mathematics

Journal of the Indian Mathematical Society Pub Date : 2018-06-01 DOI:10.18311/JIMS/2018/20123

Paula Kemp, L. Ratliff, Kishor Shah

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引用次数: 0

摘要

证明了对于所有局部环(R,M)，在R的补全^R中深度为1个最小素理想ω的集合DO(R)与R/Z的积分闭包(R/Z)'中高度为1个最大理想_m '的集合HO(R/Z)之间存在正则双射，其中Z = Rad(R)。更进一步，对于有限集D:= {V*/V*:= (^R/ω)'， ω∈DO(R)}和H:= {V/V:= (R/Z)' M'，′M'∈HO(R/Z)}:(a) D和H中的元素是离散的noether赋值环。(b) D = {^V∈H}。

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On Nagata's Result about Height One Maximal Ideals and Depth One Minimal Prime Ideals (I)

It is shown that, for all local rings (R,M), there is a canonical bijection between the set DO(R) of depth one minimal prime ideals ω in the completion ^{^}R of R and the set HO(R/Z) of height one maximal ideals ̅M' in the integral closure (R/Z)' of R/Z, where Z := Rad(R). Moreover, for the finite sets D := {V*/V* := (^{^}R/ω)', ω ∈ DO(R)} and H := {V/V := (R/Z)'_̅M', ̅M' ∈ HO(R/Z)}:

(a) The elements in D and H are discrete Noetherian valuation rings.

(b) D = {^{^}V ∈ H}.

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来源期刊

Journal of the Indian Mathematical Society Mathematics-Mathematics (all)

CiteScore

0.50

自引率

0.00%

发文量

期刊介绍： The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.