类组和 PID 的阶乘因式分解

Pub Date : 2024-07-18 DOI:10.1016/j.jnt.2024.06.008

Hyun Seung Choi

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引用次数: 0

摘要

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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Class group and factorization in orders of a PID

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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