| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Dept Matemat UFSCar, Rodovia Washington Luis 235, BR-13565905 Sao Carlos, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | Journal of Pure and Applied Algebra; v. 226, n. 6 JUN 2022. |
| Web of Science Citations: | 0 |
| Abstract | |
In this paper we study the truncation nu(q) of a valuation nu on a polynomial q. It is known that when q is a key polynomial, then nu(q) is a valuation. It is also known that the converse does not hold. We show that when q is a key polynomial, then nu(q) is the restriction of the truncation given by an optimizing root of q. We also discuss which conditions assure that nu(q) = nu. Finally, we assume that nu(q) is a valuation and present some conditions, given in terms of the graded algebra, to assure that q is a key polynomial. (C) 2021 Elsevier B.V. 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: | 20/05148-0 - The valuative tree |
| Grantee: | Caio Henrique Silva de Souza |
| Support Opportunities: | Scholarships in Brazil - Master |