On isomorphy of pure hulls of purifiable torsion-free subgroups (Q5957960)
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scientific article; zbMATH DE number 1719288
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On isomorphy of pure hulls of purifiable torsion-free subgroups |
scientific article; zbMATH DE number 1719288 |
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On isomorphy of pure hulls of purifiable torsion-free subgroups (English)
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9 July 2002
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A subgroup of an Abelian group is purifiable if it is contained in a minimal pure subgroup, a pure hull. In general, a purifiable subgroup may have non-isomorphic pure hulls, but this is not the case when the purifiable subgroup is torsion-free. Theorem. Let \(A\) be a purifiable torsion-free subgroup of the arbitrary Abelian group \(G\) and \(H\), \(H'\) pure hulls of \(A\). Then \(H\cong H'\) and \(H/A\cong H'/A\).
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torsion-free purifiable subgroups
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Abelian groups
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pure hulls
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