整数有理函数环的Krull维数

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2025-01-03 DOI:10.1007/s00013-024-02086-7

M. M. Chems-Eddin, B. Feryouch, H. Mouanis, A. Tamoussit

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引用次数: 0

摘要

设D是一个有商域K的整域，E是K的子集，E上的整值有理函数环定义为$$\begin{aligned} \mathrm {Int^R}(E,D):=\lbrace \varphi \in K(X);\; \varphi (E)\subseteq D\rbrace . \end{aligned}$$本文的主要目的是研究环的Krull维$\mathrm {Int^R}(E,D).$特别地，我们对Jaffard或pvd的域感兴趣。通过一些实例，得到了有趣的结果。

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On the Krull dimension of rings of integer-valued rational functions

Let D be an integral domain with quotient field K and E a subset of K. The ring of integer-valued rational functions on E is defined as

$$\begin{aligned} \mathrm {Int^R}(E,D):=\lbrace \varphi \in K(X);\; \varphi (E)\subseteq D\rbrace . \end{aligned}$$

The main goal of this paper is to investigate the Krull dimension of the ring $\mathrm {Int^R}(E,D).$ Particularly, we are interested in domains that are either Jaffard or PVDs. Interesting results are established with some illustrating examples.

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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.