On common extensions of valued fields

[摘要] Given a valuation v on a field K, an extension (v) over bar to an algebraic closure (K) over bar and an extension w to K(X). In this paper, we study common extensions (w) over bar of both w and (v) over bar to the field (K) over bar (X). We describe the set of valuations (w) over bar using a last key polynomial for the valuation w and its roots. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-15

[关键词] Valuation;Key polynomials;Minimal pairs;Common extensions