Valuation equivalence
= Valuation equivalence
{title2=$\mathcal O_v=\mathcal O_w$}
= Equivalent valuations
{synonym}
Two additive <valuations> are equivalent when they have the same <valuation ring>. Their ordered value-group images then identify compatibly with the <valuations>; for nontrivial real-valued rank-one <valuations> this is multiplication by a positive constant.