noether环的一个值定理

IF 0.8 3区数学 Q2 MATHEMATICS

Michigan Mathematical Journal Pub Date : 2020-11-30 DOI:10.1307/mmj/20206022

Antoni Rangachev

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引用次数: 1

摘要

设A和B是积分域。假设A是noether代数，B是包含A的有限生成的A代数，用A'表示A在B中的整闭包，我们证明A'是由有限多个唯一的离散赋值环决定的。我们的结果推广了Rees经典的理想值定理。我们还得到了Zariski主定理的一个变体。

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A Valuation Theorem for Noetherian Rings

Let A and B be integral domains. Suppose A is Noetherian and B is a finitely generated A-algebra that contains A. Denote by A' the integral closure of A in B. We show that A' is determined by finitely many unique discrete valuation rings. Our result generalizes Rees' classical valuation theorem for ideals. We also obtain a variant of Zariski's main theorem.

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来源期刊

Michigan Mathematical Journal 数学-数学

CiteScore

1.20

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Michigan Mathematical Journal is available electronically through the Project Euclid web site. The electronic version is available free to all paid subscribers. The Journal must receive from institutional subscribers a list of Internet Protocol Addresses in order for members of their institutions to have access to the online version of the Journal.