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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Rings with property $D$
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by Eben Matlis PDF
Trans. Amer. Math. Soc. 170 (1972), 437-446 Request permission

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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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 170 (1972), 437-446
  • MSC: Primary 13G05
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0306186-9
  • MathSciNet review: 0306186