Class group and factorization in orders of a PID

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-07-18 DOI:10.1016/j.jnt.2024.06.008

引用次数: 0

Abstract

In this paper, we study properties of factorization in orders of a PID via the computation of algebraic invariants that measure the failure of unique factorization. The focus is on the numerical semigroup rings over a finite field and the orders of imaginary quadratic fields with class number 1. We also give a complete description of the class group structure of those rings.

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类组和 PID 的阶乘因式分解

在本文中，我们通过计算衡量唯一因式分解失败的代数不变式，研究了因式分解在 PID 阶中的性质。重点是有限域上的数值半群环和类数为 1 的虚二次域的阶。我们还给出了这些环的类群结构的完整描述。

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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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.