Additive structure of totally positive quadratic integers

被引：5

作者：

Hejda, Tomas ^{[1
,2
]}

Kala, Vitezslav ^{[1
]}

机构：

[1] Charles Univ Prague, Dept Algebra, FMP, Sokolovska 49-83, Prague 18600, Czech Republic

[2] Univ Chem & Technol, FCE, Dept Math, Studentska 2031-6, Prague 16000, Czech Republic

来源：

MANUSCRIPTA MATHEMATICA | 2020年 / 163卷 / 1-2期

关键词：

11R11; 11A55; 20M05; 20M14; REAL; FORMS; NUMBERS; RANK;

D O I：

10.1007/s00229-019-01143-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

LetK=Q(D)\documentclass be a real quadratic field. We consider the additive semigroupOK+(+)\documentclass of totally positive integers inKand determine its generators (indecomposable integers) and relations; they can be nicely described in terms of the periodic continued fraction forD\documentclass. We also characterize all uniquely decomposable integers inKand estimate their norms. Using these results, we prove that the semigroupOK+(+)\documentclass completely determines the real quadratic fieldK.

引用

页码：263 / 278

页数：16

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