摘要 : For a fixed irreducible polynomial F we study the set nu(F) of all valuations on K [x] bounded by valuations whose support is (F). The first main result presents a characterization for valuations in nu(F) in terms of their graded ... 展开 For a fixed irreducible polynomial F we study the set nu(F) of all valuations on K [x] bounded by valuations whose support is (F). The first main result presents a characterization for valuations in nu(F) in terms of their graded rings. We also present a result which gives, for a fixed nu is an element of nu(F) and a key polynomial Q is an element of KP(nu), the maximum value that augmented valuations in nu(F) can assume on Q. This value is presented explicitly in terms of the slopes of the Newton polygon of F with respect to Q. Finally, we present some results about Artin-Schreier extensions that illustrate the applications that we have in mind for the results in this paper. (C) 2021 Elsevier Inc. All rights reserved. 收起