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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
DOI: https://doi.org/10.1090/S0002-9939-1976-0409448-9
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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Keywords: Coherence, descent of flatness, <IMG WIDTH="69" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$D + M$"> construction, valuation ring
Article copyright: © Copyright 1976 American Mathematical Society