On the implicit constant fields and key polynomials for valuation algebraic extensions

DOI10.1216/JCA.2022.14.515arXiv2111.14344MaRDI QIDQ6384179

Publication date: 29 November 2021

Abstract: This article is a natural construction of our previous works. In this article, we employ similar ideas due to MacLane to provide an estimate of IC(K(X)|K,v) when (K(X)|K,v) is a valuation algebraic extension. Our central result is an analogue of the estimate obtained in the valuation transcendental case. We further provide a natural construction of a complete sequence of key polynomials for v over K in the setting of valuation algebraic extensions.

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Non-Archimedean valued fields (12J25) General valuation theory for fields (12J20)

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