Torsion-free Abelian Groups Revisited
| Autor: | Schultz, Phill |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let G be a torsion--free abelian group of finite rank. The automorphism group Aut(G) acts on the set of maximal independent subsets of G. The orbits of this action are the isomorphism classes of indecomposable decompositions of G. G contains a direct sum of strongly indecomposable groups as a characteristic subgroup of finite index, giving rise to a classification of finite rank strongly indecomposable torsion--free abelian groups. Comment: In Section 5, The quasi--category of V, I erroneously concluded that the unit group of the ring $Q\otimes End(G)$ is $Q^*.Aut(G)$. This dumb error led to several false statements, so I wish to withdraw and re-write the whole paper |
| Databáze: | arXiv |
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