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

Rings with property $ D$


Author: Eben Matlis
Journal: Trans. Amer. Math. Soc. 170 (1972), 437-446
MSC: Primary 13G05
MathSciNet review: 0306186
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Abstract: An integral domain is said to have property $ {\text{D}}$ if every torsion-free module of finite rank is a direct sum of modules of rank one. In recent papers the author has given partial solutions to the problem of finding all rings with this property. In this paper the author is finally able to show that an integrally closed integral domain has property $ {\text{D}}$ if and only if it is the intersection of at most two maximal valuation rings.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0306186-9
PII: S 0002-9947(1972)0306186-9
Keywords: Maximal valuation ring, torsion-free module, direct sum decomposition
Article copyright: © Copyright 1972 American Mathematical Society