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Extensions of discrete valuations
*September 5, 2009*

*Posted by Akhil Mathew in algebra, algebraic number theory, commutative algebra, number theory.*

Tags: absolute values, Dedekind domains, discrete valuation rings, separable extensions

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Tags: absolute values, Dedekind domains, discrete valuation rings, separable extensions

add a comment

With the school year starting, I can’t keep up with the one-post-a-day frequency anymore. Still, I want to keep plowing ahead towards class field theory.

Today’s main goal is to show that under certain conditions, we can always extend valuations to bigger fields. I’m not aiming for maximum generality here though.

**Dedekind Domains and Extensions **

One of the reasons Dedekind domains are so important is

Theorem 1Let be a Dedekind domain with quotient field , a finite separable extension of , and the integral closure of in . Then is Dedekind. (more…)

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