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arXiv · 2111.14344

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

Arpan Dutta
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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.

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Arpan Dutta. 2021-11-29. On the implicit constant fields and key polynomials for valuation algebraic extensions. https://arxiv.org/abs/2111.14344

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