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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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When is $D+M$ coherent?
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by David E. Dobbs and Ira J. Papick PDF
Proc. Amer. Math. Soc. 56 (1976), 51-54 Request permission

Abstract:

Let $V$ be a valuation ring of the form $K + M$, where $K$ is a field and $M( \ne 0)$ is the maximal ideal of $V$. Let $D$ be a proper subring of $K$. Necessary and sufficient conditions are given that the ring $D + M$ be coherent. The condition that a given ideal of $V$ be $D + M$-flat is also characterized.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 56 (1976), 51-54
  • MSC: Primary 13G05
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0409448-9
  • MathSciNet review: 0409448