Remark on coefficient fields in complete local rings
نویسندگان
چکیده
منابع مشابه
Complete fields and valuation rings
In order to make further progress in our investigation of finite extensions L/K of the fraction field K of a Dedekind domain A, and in particular, to determine the primes p of K that ramify in L, we introduce a new tool that allows us to “localize” fields. We have seen how useful it can be to localize the ring A at a prime ideal p: this yields a discrete valuation ring Ap, a principal ideal dom...
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The purpose of this note is to provide for my algebra class a guide to the proof of Cohen's structure theorem for complete local rings as given by Cohen himself, in the original 1946 paper [C]. In spite of more modern and concise treatments by the likes of Nagata and Grothendieck, the original proof is a model of clarity and the entire paper is a commutative algebra masterpiece. First, a few wo...
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ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 1965
ISSN: 2156-2261
DOI: 10.1215/kjm/1250524609