Valuations on K[x] approaching a fixed irreducible polynomial

Barnabe, Matheus dos S.; Novacoski, Josnei

doi:10.1016/j.jalgebra.2021.10.041

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Totally Ordered Sets Of Valuations and Direct Limits1

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2022

2024

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Cited by 5 publications

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“…Proposition 4.6. (Corollary 2.3 of [14]) Let {ν i } i∈I be a totally ordered set in V. For every f ∈ K[x] we have that either {ν i (f )} i∈I is strictly increasing, or there exists i 0 ∈ I such that ν i (f ) = ν i0 (f ) for every i ∈ I with i ≥ i 0 .…”

Section: Totally Ordered Sets Of Valuations and Direct Limitsmentioning

confidence: 99%

Graded rings associated to valuations and direct limits

de Souza,

Novacoski,

Spivakovsky

2022

Preprint

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In this paper, we study the structure of the graded ring associated to a limit key polynomial Qn in terms of the key polynomials that define Qn. 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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Section: Totally Ordered Sets Of Valuations and Direct Limitsmentioning

confidence: 99%