论理想一元群的算术

IF 0.8 4区数学 Q2 MATHEMATICS

Arkiv for Matematik Pub Date : 2021-06-02 DOI:10.4310/arkiv.2022.v60.n1.a4

A. Geroldinger, M. A. Khadam

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引用次数: 9

摘要

研究了Krull和弱Krull Mori域可逆理想(更确切地说，是某些理想系统r的r可逆理想)的模群的代数和算术结构。我们也研究了noether域上至少有两个不定数的多项式环的所有非零理想的幺群。其中，我们证明了它们不是迁移Krull，但它们与具有无限类群和所有类的素数的Krull模群有几个相同的算术现象。

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On the arithmetic of monoids of ideals

We study the algebraic and arithmetic structure of monoids of invertible ideals (more precisely, of r-invertible r-ideals for certain ideal systems r) of Krull and weakly Krull Mori domains. We also investigate monoids of all nonzero ideals of polynomial rings with at least two indeterminates over noetherian domains. Among others, we show that they are not transfer Krull but they share several arithmetic phenomena with Krull monoids having infinite class group and prime divisors in all classes.

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来源期刊

Arkiv for Matematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishing research papers, of short to moderate length, in all fields of mathematics.