Rings with property 𝐷

Matlis, Eben

doi:10.1090/S0002-9947-1972-0306186-9

Rings with property $D$
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by Eben Matlis

Trans. Amer. Math. Soc. 170 (1972), 437-446

DOI: https://doi.org/10.1090/S0002-9947-1972-0306186-9

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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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