On valuation rings that contain zero divisors
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- by James A. Huckaba PDF
- Proc. Amer. Math. Soc. 40 (1973), 9-15 Request permission
Abstract:
Let $R$ be a commutative ring with identity. A new proof is given of the theorem due to Samuel and Griffin which states that $R$ is integrally closed in its total quotient ring if and only if $R$ is the intersection of $B$-valuation rings. We then prove the main result of the paper: If $K$ is a $\pi$-regular ring, then $K$ admits only Prüfer rings as valuation rings.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 9-15
- MSC: Primary 13F05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0318134-2
- MathSciNet review: 0318134