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On the degree of repeated radical extensions

Part of: General field theory Field extensions

Published online by Cambridge University Press:  23 November 2020

Fernando Szechtman
Fernando Szechtman*
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina, SK, Canada
*
e-mail:[email protected]
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Abstract

We answer a question posed by Mordell in 1953, in the case of repeated radical extensions, and find necessary and sufficient conditions for $[F[\sqrt [m_1]{N_1},\dots ,\sqrt [m_\ell ]{N_\ell }]:F]=m_1\cdots m_\ell $ , where F is an arbitrary field of characteristic not dividing any $m_i$ .

Keywords

Radical extensionGalois extensionVahlen-Capelli irreducibility criterion

MSC classification

Primary: 12F05: Algebraic extensions
Secondary: 12F10: Separable extensions, Galois theory 12E05: Polynomials (irreducibility, etc.)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 4 , December 2021 , pp. 877 - 885
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

This paper is dedicated to Natalio H. Guersenzvaig. This research was partially supported by an NSERC grant.

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