When is 𝐷+𝑀 coherent?

Dobbs, David E.; Papick, Ira J.

doi:10.1090/S0002-9939-1976-0409448-9

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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