Lemma 10.50.14. Let $A$ be a valuation ring. The valuation $v : A -\{ 0\} \to \Gamma _{\geq 0}$ has the following properties:

1. $v(a) = 0 \Leftrightarrow a \in A^*$,

2. $v(ab) = v(a) + v(b)$,

3. $v(a + b) \geq \min (v(a), v(b))$.

Proof. Omitted. $\square$

Comment #43 by Rankeya on

valution should be valuation

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