| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Fed Sao Carlos, Dept Matemat, Rodovia Washington Luis 235, BR-13565905 Sao Carlos, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | Journal of Algebra; v. 592, p. 100-117, FEB 15 2022. |
| Web of Science Citations: | 0 |
| Abstract | |
For a fixed irreducible polynomial F we study the set nu(F) of all valuations on K {[}x] bounded by valuations whose support is (F). The first main result presents a characterization for valuations in nu(F) in terms of their graded rings. We also present a result which gives, for a fixed nu is an element of nu(F) and a key polynomial Q is an element of KP(nu), the maximum value that augmented valuations in nu(F) can assume on Q. This value is presented explicitly in terms of the slopes of the Newton polygon of F with respect to Q. Finally, we present some results about Artin-Schreier extensions that illustrate the applications that we have in mind for the results in this paper. (C) 2021 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 |