Key polynomials and preminimal pairs
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- by
Yu. L. Ershov;
Translated by: S. V. Kislyakov - St. Petersburg Math. J. 35 (2024), 461-465
- DOI: https://doi.org/10.1090/spmj/1812
- Published electronically: July 30, 2024
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Abstract:
The paper pertains to the theory of valued fields and is devoted to describing extensions of valuations to the field of rational functions in one variable. An efficient tool here is the notion of a key polynomial introduced by S. Maclane in 1936. With the use of the notion of a preminimal pair introduced recently, a new description of key polynomials over Henselian fields is found.References
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Bibliographic Information
- Yu. L. Ershov
- Affiliation: S. L. Sobolev Institute of Mathematics SO RAN, Academician Koptyug pr. 4, Novosibirsk 630090, Russia
- Email: ershov@math.nsc.ru
- Received by editor(s): August 15, 2022
- Published electronically: July 30, 2024
- Additional Notes: This work was done as part of the state assignment of IM SORAN (project no. FWNF-2022-0012)
- © Copyright 2024 American Mathematical Society
- Journal: St. Petersburg Math. J. 35 (2024), 461-465
- MSC (2020): Primary 12J10
- DOI: https://doi.org/10.1090/spmj/1812