Equivalence and isomorphy of prolongation of valuations on simply transcendental extensions (Q5953575)

Let \(K\) be a field, and let \(t\) be transcendental over \(K\). It is known that there are three types of prolongations of valuations from \(K\) to \(K(t)\). Let \(\overline{K}\) be an algebraic closure of \(K\). With the help of \(\overline{K}\) the authors give a representation of the equivalence and isomorphy classes of each type. Upper and lower bounds for the cardinalities for these classes are deduced. Reviewer's remark: It is a pity that the authors did not write their interesting paper in English.