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Article Dans Une Revue Journal of Pure and Applied Algebra Année : 2023

Graded rings associated to valuations and direct limits

Résumé

In this paper, we study the structure of the graded ring associated to a limit key polynomial $Q_n$ in terms of the key polynomials that define $Q_n$. In order to do that, we use direct limits. In general, we describe the direct limit of a family of graded rings associated to a totally ordered set of valuations. As an example, we describe the graded ring associated to a valuation-algebraic valuation as a direct limit of graded rings associated to residue-transcendental valuations.
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Dates et versions

hal-03755057 , version 1 (27-11-2022)

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C.H. Silva de Souza, J.A. Novacoski, Mark Spivakovsky. Graded rings associated to valuations and direct limits. Journal of Pure and Applied Algebra, 2023, 227 (5), pp.107296. ⟨10.1016/j.jpaa.2022.107296⟩. ⟨hal-03755057⟩
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