Let be a field. The equivalence of valuations and of may be defined so that
is not the trivial valuation;
It it easy to see that these conditions imply for both valuations (use ). Also, we have always
so both valuations have a common valuation ring in the case they are non-archimedean. (The of the more general Krull valuations is defined to that they have common valuation rings.) Further, both valuations determine a common metric on .
Two valuations (of rank (http://planetmath.org/KrullValuation) one) and of are iff one of them is a positive power of the other,
where is a positive .
|Date of creation||2013-03-22 14:25:27|
|Last modified on||2013-03-22 14:25:27|
|Last modified by||pahio (2872)|
|Defines||equivalence of valuations|