作者
Michal Hrbek, Pavel Růžička
发表日期
2015/1/2
期刊
Quaestiones Mathematicae
卷号
38
期号
1
页码范围
103-120
出版商
Taylor & Francis
简介
We characterize Abelian groups with a minimal generating set: Let τ A denote the maximal torsion subgroup of A. An infinitely generated Abelian group A of cardinality κ has a minimal generating set iff at least one of the following conditions is satisfied:
- dim(A/pA) = dim(A/qA) = κ for at least two different primes p, q.
- dim(t A/pt A) = κ for some prime number p.
- Σ{dim(A/(pA + B)) ∣ dim(A/(pA + B)) < κ} = κ for every finitely generated subgroup B of A.
学术搜索中的文章
M Hrbek, P Růžička - Quaestiones Mathematicae, 2015