Hensel’s lemma and a classification theorem September 2, 2009Posted by Akhil Mathew in algebraic number theory, algebra, number theory, commutative algebra.
Tags: discrete valuation rings, Hensel's lemma, characteristic zero
So, I’ll discuss the proof of a classification theorem that DVRs are often power series rings, using Hensel’s lemma.
Systems of representatives
The main result that we have today is:
Theorem 1 Suppose is of characteristic zero. Then , the power series ring in one variable, with respect to the usual discrete valuation on . (more…)