Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 13.40

Retrieve articles in all journals with MSC: 13.40

Additional Information

Keywords: Prüfer domains, categories, equivalence, functor, torsion-free modules, rank, tensor-product, linearly independent sets, completely decomposable
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society