Nice bases for mixed and torsion-free Abelian groups. (Q708462)
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scientific article; zbMATH DE number 5799920
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nice bases for mixed and torsion-free Abelian groups. |
scientific article; zbMATH DE number 5799920 |
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Nice bases for mixed and torsion-free Abelian groups. (English)
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14 October 2010
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An Abelian group \(G\) has a nice basis if \(G\) is the union of an ascending chain of direct sums of cyclic groups, each of which is nice in \(G\). The concept was introduced in the context of totally projective \(p\)-groups, but in this paper, Danchev considers arbitrary Abelian groups. He shows that divisible groups and global Warfield groups have nice bases, and finds examples of torsion-free and mixed groups which do not. He also considers the related concepts of weak and strong nice bases.
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weak nice bases
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strong nice bases
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weakly nice subgroups
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strongly nice subgroups
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algebraically compact groups
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Warfield groups
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totally projective groups
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direct sums of cyclic groups
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0.9006232
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0.87377524
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0.87028146
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0.86858374
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