Noetherian域的积分闭包与Rees值环的交集，（II）

Q4 Mathematics

Journal of the Indian Mathematical Society Pub Date : 2017-01-02 DOI:10.18311/jims/2017/6108

Paula Kemp, L. Ratliff, Kishor Shah

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引用次数: 0

摘要

设1 < s 1 <…< s k为整数，且假设k≥2(因此s k≤3)，则存在一个局部UFD (Unique Factorization Domain) (R,M)使得:(1)Height(M) = s k。(2) R = R ' =∩{VI V (V, N)€j}, V j (j = 1,。， κ)是M个基本理想的所有Rees估值环(V,N)的集合，使得trd((vi N) I (ri M)) = s j - 1。(3)有了v1，…， V κ as in (2)， v1∪…V κ是所有m -初级理想的所有Rees估值环的不相交并，并且每个m -初级理想在每个V j中至少有一个Rees估值环。

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Integral Closure of Noetherian Domains and Intersections of Rees Valuation Rings, (II)

Let 1 < s 1 < . . . < s k be integers, and assume that κ ≥ 2 (so s k ≤ 3). Then there exists a local UFD (Unique Factorization Domain) (R,M) such that: (1) Height(M) = s k . (2) R = R' = ∩{VI (V,N) € V j }, where V j (j = 1, . . . , κ) is the set of all of the Rees valuation rings (V,N) of the M-primary ideals such that trd((V I N) I (R I M)) = s j - 1. (3) With V 1 , . . . , V κ as in (2), V 1 ∪ . . . V κ is a disjoint union of all of the Rees valuation rings of allof the M-primary ideals, and each M-primary ideal has at least one Rees valuation ring in each V j .

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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.