Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T03:13:43.844Z Has data issue: false hasContentIssue false
  • English
  • Français

Solvability by Real Radicals and Fermat Primes

Published online by Cambridge University Press:  20 November 2018

C. U. Jensen
C. U. Jensen*
Affiliation:
Department of Mathematics University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen Denmark, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a survey of old and new results concerning the expressibility of the real roots of a solvable polynomial over a real number field by real radicals. A characterization of Fermat primes is obtained in terms of solvability by real radicals for certain ploynomials.

Keywords

12E0512F10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 2 , 01 June 2004 , pp. 229 - 236
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Barrera-Moro, F. and Lam-Estrada, P., Radical extensions and crossed homomorphisms. Bull. Austral. Math. Soc. 64 (2001), 107–119.Google Scholar
[2] Barrera-Moro, F. and Vélez, W. Y., Some results on radical extensions. J. Algebra 162 (1993), 295–301.Google Scholar
[3] Birch, J. B., Cyclotomic Fields and Kummer Extensions. In: Algebraic Number Theory, (eds., W. Cassels and A. Fröhlich), Academic Press, 1967, 85–93.Google Scholar
[4] Fried, M. D. and Jarden, M., Field Arithmetic. Springer, 1986.Google Scholar
[5] Isaacs, I. M. and Moulton, D. P.,Real fields and repeated radical extensions. J. Algebra 201 (1998), 429–455.Google Scholar
[6] Jensen, C. U., A Remark on Real Radical Extensions. Acta Arith. 107 (2003), 373–379.Google Scholar
[7] Lang, S., Algebra. Addison-Wesley, 1965.Google Scholar
[8] Loewy, A., Über die Reduktion algebraischer Gleichungen durch Adjunktion insbesondere reeller Radikale.Math. Z. 15 (1922), 261–273.Google Scholar
[9] van der Waerden, B. L., Algebra I. Springer, 1976.Google Scholar