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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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