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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

When is $ D+M$ coherent?


Authors: David E. Dobbs and Ira J. Papick
Journal: Proc. Amer. Math. Soc. 56 (1976), 51-54
MSC: Primary 13G05
MathSciNet review: 0409448
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0409448-9
PII: S 0002-9939(1976)0409448-9
Keywords: Coherence, descent of flatness, $ D + M$ construction, valuation ring
Article copyright: © Copyright 1976 American Mathematical Society