Valuation (algebra)

Instead of ∞, we adjoin a formal symbol O to Γ, with the ordering and group law extended by the rules

(Note that the directions of the inequalities are reversed from those in the additive notation.)

In this article, we use the terms defined above, in the additive notation. However, some authors use alternative terms:

Two valuations of K are equivalent if and only if they have the same valuation ring.