Abstract
This note concerns the study of torsion-free modules of rank 2 over an almost maximal valuation domain R, and we give complete and independent systems of invariants for those torsion-free rank 2 modules whose basic submodules are of rank 1.
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References
L. FUCHS, On subdirect unions, Acta Math. Acad. Sci. Hung. 3 (1952), 103–120.
L. FUCHS, Modules over valuation rings (Preprint).
L. FUCHS and L. SALCE, Prebasic submodules over valuation rings (to appear).
L. FUCHS and G. VILJOEN, On finite rank torsion-free modules over almost maximal valuation domains (to appear).
D.T. GILL, Almost maximal valuation rings, J. London Math. Soc. 4 (1971), 140–146
I. KAPLANSKY, Modules over Dedekind rings and valuation rings, Trans. AMS 72 (2) (1952), 327–340.
S. MACLANE, Homology, Springer Verlag, Berlin 1963.
E. MATLIS, Injective modules over Prüfer rings, Nagoya Math. J. (1959), 57–69.
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© 1983 Springer-Verlag Berlin Heidelberg
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Viljoen, G. (1983). On Torsion-Free Modules of Rank 2 over an Almost Maximal Valuation Domain. In: Göbel, R., Lady, L., Mader, A. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 1006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21560-9_42
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DOI: https://doi.org/10.1007/978-3-662-21560-9_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12335-4
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