Key polynomials and pseudo-convergent sequences

Autor(es)

Novacoski, Josnei ^[1] ; Spivakovsky, Mark ^{[2, 3, 4]}

Afiliação do(s) autor(es)

^[1] ICMC USP, Av Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos, SP - Brazil

^[2] CNRS, 118 Rte Narbonne, F-31062 Toulouse 9 - France

^[3] Inst Math, 118 Rte Narbonne, F-31062 Toulouse 9 - France

^[4] Univ Nacl Autonoma Mexico, Unidad Cuernavaca, Inst Math, Av Univ S-N Col Lomas Chamilpa, Codigo Postal 6221, Cuernavaca, Morelos - Mexico

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 495, p. 199-219, FEB 1 2018.
• Citações Web of Science: 2

Resumo

In this paper we introduce a new concept of key polynomials for a given valuation v on K {[}x]. We prove that such polynomials have many of the expected properties of key polynomials as those defined by MacLane and Vaquie, for instance, that they are irreducible and that the truncation of v associated to each key polynomial is a valuation. Moreover, we prove that every valuation v on K {[}x] admits a sequence of key polynomials that completely determines v (in the sense which we make precise in the paper). We also establish the relation between these key polynomials and pseudo convergent sequences defined by Kaplansky. (C) 2017 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 15/23409-7 - Comparação entre os diferentes programas para uniformização local
• Beneficiário: Josnei Antonio Novacoski
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado