加性不可分解的正定积分格

IF 0.8 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2025-01-24 DOI:10.1007/s10114-025-2562-6

Ruiqing Wang

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引用次数: 0

摘要

本文给出了具有2、3、4、5在\({\mathbb Z}\)上的判别式的不可分解正定积分格是可加不可分解格的几个充要条件。利用这些结果，我们证明了除35个例外情况外，存在具有判别式为2、3、4、5且秩大于等于2的可加不可分解的正积分二次格。在例外情况下，没有晶格具有期望的性质。给出了可加不可分解正定积分格的一个提升定理。

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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Additively Indecomposable Positive Definite Integral Lattices

In this paper, we obtain some sufficient and necessary conditions for indecomposable positive definite integral lattices with discriminants 2, 3, 4 and 5 over \({\mathbb Z}\) being additively indecomposable lattices. Using these results, we prove that there exist additively indecomposable positive integral quadratic lattices with discriminants 2, 3, 4 and 5 and rank greater than or equal to 2 but for 35 exceptions. In the exceptions there are no lattices with the desired properties. We also give a lifting theorem of additively indecomposable positive definite integral lattices.

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.