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Algebra i Analiz, 2023, Volume 35, Issue 3, Pages 38–43 (Mi aa1866)  
Research Papers

Key polynomials and preminimal pairs

Yu. L. Ershov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
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Abstract: The paper is in theory of valued fields and devoted to questions of describing extentions valuations of a field on its field of rational functions in one variable.One of effective tools for descriptions of such extentions is the notion of key polynomial introduced by S,Maclane in 1936 year.Using the notion of preminimal pair introduced recently new characterisation of key polynomials over henselian fields was obtained.
Keywords: key polynomial, preminimal pair, valued fields, henselian fields.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0012
Received: 15.08.2022
English version:
St. Petersburg Mathematical Journal, 2024, Volume 35, Issue 3, Pages 461–465
DOI: https://doi.org/10.1090/spmj/1812
Document Type: Article
Language: Russian
Citation: Yu. L. Ershov, “Key polynomials and preminimal pairs”, Algebra i Analiz, 35:3 (2023), 38–43; St. Petersburg Math. J., 35:3 (2024), 461–465
Citation in format AMSBIB
\Bibitem{Ers23}
\by Yu.~L.~Ershov
\paper Key polynomials and preminimal pairs
\jour Algebra i Analiz
\yr 2023
\vol 35
\issue 3
\pages 38--43
\mathnet{http://mi.mathnet.ru/aa1866}
\transl
\jour St. Petersburg Math. J.
\yr 2024
\vol 35
\issue 3
\pages 461--465
\crossref{https://doi.org/10.1090/spmj/1812}
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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