KEY POLYNOMIALS, SEPARATE AND IMMEDIATE VALUATIONS, AND SIMPLE EXTENSIONS OF VALUED FIELDS

Gérard Leloup (1)

1 LMM - Laboratoire Manceau de Mathématiques

We give a first-order definition of key polynomials, we show the links with previous definitions, that it is relevant to study key degrees, and to use a kind of valuations that we call partially multiplicative. We also prove or reprove several properties.

Mots clés: simple extension; valuation; key polynomial

Domaines: Algèbre commutative [math.AC]

Gérard Leloup. KEY POLYNOMIALS, SEPARATE AND IMMEDIATE VALUATIONS, AND SIMPLE EXTENSIONS OF VALUED FIELDS. 2022. ⟨hal-01876056v3⟩