初等除数、霍赫斯特对偶性和光谱

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-09-28 DOI:10.1007/s00013-024-02052-3

Wolfgang Rump

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引用次数: 0

摘要

研究证明，每个贝祖特域都可以嵌入到具有相同可分性群的初等除数域中。因此，一个贝祖特域的素谱与一个初等除数域的素谱是同构的。结合之前的一个结果，我们可以得出，当且仅当一个拓扑空间是一个序列准紧密的（T_1\）空间时，它与一个初等除数域的最大谱是同构的。

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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Elementary divisors, Hochster duality, and spectra

It is proved that every Bézout domain admits an embedding into an elementary divisor domain with the same divisibility group. So the prime spectrum of a Bézout domain is homeomorphic to the prime spectrum of an elementary divisor domain. Together with an earlier result, it follows that a topological space is homeomorphic to the maximal spectrum of an elementary divisor domain if and only if it is a serial quasi-compact \(T_1\)-space.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.