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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Modules over Prüfer domains


Author: Syed M. Fakhruddin
Journal: Trans. Amer. Math. Soc. 159 (1971), 469-487
MSC: Primary 13.40
MathSciNet review: 0279084
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Abstract: We prove that the category of torsion-free modules over a Prüfer domain is equivalent to a certain category of diagrams. As applications we derive (i) a strong version of Baer-Kulikov-Kaplansky theorem for modules over a valuation ring, (ii) the determination of a complete set of invariants for modules of almost countable rank over an almost-maximal valuation ring, (iii) a new nonhomological proof of the characterization of a maximal valuation ring due to Matlis.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0279084-6
PII: S 0002-9947(1971)0279084-6
Keywords: Prüfer domains, categories, equivalence, functor, torsion-free modules, rank, tensor-product, linearly independent sets, completely decomposable
Article copyright: © Copyright 1971 American Mathematical Society