Solvability by Real Radicals and Fermat Primes
Canadian mathematical bulletin, Tome 47 (2004) no. 2, pp. 229-236

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2004-022-9
Mots-clés : 12E05, 12F10
Jensen, C. U. Solvability by Real Radicals and Fermat Primes. Canadian mathematical bulletin, Tome 47 (2004) no. 2, pp. 229-236. doi: 10.4153/CMB-2004-022-9
@article{10_4153_CMB_2004_022_9,
     author = {Jensen, C. U.},
     title = {Solvability by {Real} {Radicals} and {Fermat} {Primes}},
     journal = {Canadian mathematical bulletin},
     pages = {229--236},
     year = {2004},
     volume = {47},
     number = {2},
     doi = {10.4153/CMB-2004-022-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-022-9/}
}
TY  - JOUR
AU  - Jensen, C. U.
TI  - Solvability by Real Radicals and Fermat Primes
JO  - Canadian mathematical bulletin
PY  - 2004
SP  - 229
EP  - 236
VL  - 47
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-022-9/
DO  - 10.4153/CMB-2004-022-9
ID  - 10_4153_CMB_2004_022_9
ER  - 
%0 Journal Article
%A Jensen, C. U.
%T Solvability by Real Radicals and Fermat Primes
%J Canadian mathematical bulletin
%D 2004
%P 229-236
%V 47
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-022-9/
%R 10.4153/CMB-2004-022-9
%F 10_4153_CMB_2004_022_9

[1] [1] Barrera-Moro, F. and Lam-Estrada, P., Radical extensions and crossed homomorphisms. Bull. Austral. Math. Soc. 64 (2001), 107–119. Google Scholar

[2] [2] Barrera-Moro, F. and Vélez, W. Y., Some results on radical extensions. J. Algebra 162 (1993), 295–301. Google Scholar

[3] [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] [4] Fried, M. D. and Jarden, M., Field Arithmetic. Springer, 1986. Google Scholar

[5] [5] Isaacs, I. M. and Moulton, D. P.,Real fields and repeated radical extensions. J. Algebra 201 (1998), 429–455. Google Scholar

[6] [6] Jensen, C. U., A Remark on Real Radical Extensions. Acta Arith. 107 (2003), 373–379. Google Scholar

[7] [7] Lang, S., Algebra. Addison-Wesley, 1965. Google Scholar

[8] [8] Loewy, A., Über die Reduktion algebraischer Gleichungen durch Adjunktion insbesondere reeller Radikale.Math. Z. 15 (1922), 261–273. Google Scholar

[9] [9] van der Waerden, B. L., Algebra I. Springer, 1976. Google Scholar

Cité par Sources :