| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [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
Total Affiliations: 4
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| Document type: | Journal article |
| Source: | Journal of Algebra; v. 495, p. 199-219, FEB 1 2018. |
| Web of Science Citations: | 2 |
| Abstract | |
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) | |
| FAPESP's process: | 15/23409-7 - Comparison between the different programs for local uniformization |
| Grantee: | Josnei Antonio Novacoski |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |