Journal of Commutative Algebra

Hensel's lemma and the intermediate value theorem over a non-Archimedean field

Luigi Corgnier, Carla Massaza, and Paolo Valabrega

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Abstract

This paper proves that all power series over a maximal ordered Cauchy complete non-Archimedean field satisfy the intermediate value theorem on every closed interval. Hensel's lemma for restricted power series is the main tool of the proof.

Article information

Source
J. Commut. Algebra, Volume 9, Number 2 (2017), 185-211.

Dates
First available in Project Euclid: 3 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.jca/1496476821

Digital Object Identifier
doi:10.1216/JCA-2017-9-2-185

Mathematical Reviews number (MathSciNet)
MR3659948

Zentralblatt MATH identifier
1376.12011

Subjects
Primary: 12J15: Ordered fields

Keywords
non-Archimedean fields power series intermediate value Hensel's lemma

Citation

Corgnier, Luigi; Massaza, Carla; Valabrega, Paolo. Hensel's lemma and the intermediate value theorem over a non-Archimedean field. J. Commut. Algebra 9 (2017), no. 2, 185--211. doi:10.1216/JCA-2017-9-2-185. https://projecteuclid.org/euclid.jca/1496476821


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