| Full text | |
| Author(s): |
Novacoski, Josnei
Total Authors: 1
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| Document type: | Journal article |
| Source: | Journal of Algebra; v. 523, p. 1-14, APR 1 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
In this paper we establish the relation between key polynomials (as defined in {[}12]) and minimal pairs of definition of a valuation. We also discuss truncations of valuations on a polynomial ring K{[}x]. We prove that a valuation nu is equal to its truncation on some polynomial if and only if nu is valuation-transcendental. Another important result of this paper is that if mu is any extension of nu to (K) over bar {[}x] and Lambda is a complete sequence of key polynomials for nu, without last element, then for each Q is an element of Lambda there exists a suitable root a(Q) is an element of (K) over bar of Q such that [a(Q)](Q is an element of Lambda) is a pseudo-convergent sequence defining mu. (C) 2019 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 17/17835-9 - The relation between toric geometry, theory of local blow-ups and ramification theory and their applications in valuation theory |
| Grantee: | Josnei Antonio Novacoski |
| Support Opportunities: | Research Grants - Young Investigators Grants |
| 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 |