Globalization of some local properties in Krull domains
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- by D. D. Anderson PDF
- Proc. Amer. Math. Soc. 85 (1982), 141-145 Request permission
Abstract:
Let $R$ be a Krull domain. It is shown that a nonzero locally principal ideal is invertible. This is used to show that ${\text {Cl}}(R)/{\text {Pic}}(R)$ is torsion if and only if ${\text {Cl}}({R_M})$ is torsion for each maximal ideal $M$ of $R$. Here ${\text {Cl}}(R)$ and ${\text {Pic}}(R)$ denote the divisor class group and Picard group of $R$, respectively.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 141-145
- MSC: Primary 13F15; Secondary 13C12
- DOI: https://doi.org/10.1090/S0002-9939-1982-0652428-1
- MathSciNet review: 652428