RATIONAL RINGS RELATED TO WEAKLY TRANSITIVE TORSION-FREE ABELIAN GROUPS

被引：1

作者：

Meehan, Chris ^{[1
]}

Struengmann, Lutz ^{[2
]}

机构：

[1] Dublin Inst Technol, Dept Math Stat & Comp Sci, Dublin 8, Ireland

[2] Univ Duisburg Essen, Dept Math, D-45117 Essen, Germany

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2009年 / 8卷 / 05期

关键词：

Unit sum number; weak transitivity; rational group; Dirichlet's theorem; separable groups; Euler function;

D O I：

10.1142/S0219498809003576

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study subgroups R of the rational numbers Q having the property that for every pair of integers m, n such that gcd(m, n) = 1 and gcd(m, p) = gcd(n, p) = 1 whenever p is in the spectrum of R there is a unit u of R and an element r is an element of R such that un + rm - 1. These rings are closely related to weakly transitive separable groups. We prove that the property is dependent on the spectrum of the rational group in question and that the spectrum may be very complicated.

引用

页码：723 / 732

页数：10

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