Primitive complete normal bases for regular extensions
Glasgow mathematical journal, Tome 43 (2001) no. 3, pp. 383-398
Voir la notice de l'article provenant de la source Cambridge University Press
The extension E of degree n over the Galois field F={\text GF}(q)} is called regular over F, if {\text ord}_r(q) and n have greatest common divisor 1 for all prime divisors r of n which are different from the characteristic p of F (here, \order{r}{q} denotes the multiplicative order of q modulo r). Under the assumption that E is regular over F and that q-1 is divisible by 4 if q is odd and n is even, we prove the existence of a primitive element w \in E which is also completely normal over F (the latter means that w simultaneously generates a normal basis for E over every intermediate field K of E/F). Our result achieves, for the class of extensions under consideration, a common generalization of the theorem of Lenstra and Schoof on the existence of primitive normal bases [12] and the theorem of Blessenohl and Johnsen on the existence of complete normal bases [1].
Hachenberger, Dirk. Primitive complete normal bases for regular extensions. Glasgow mathematical journal, Tome 43 (2001) no. 3, pp. 383-398. doi: 10.1017/S0017089501030026
@article{10_1017_S0017089501030026,
author = {Hachenberger, Dirk},
title = {Primitive complete normal bases for regular extensions},
journal = {Glasgow mathematical journal},
pages = {383--398},
year = {2001},
volume = {43},
number = {3},
doi = {10.1017/S0017089501030026},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089501030026/}
}
TY - JOUR AU - Hachenberger, Dirk TI - Primitive complete normal bases for regular extensions JO - Glasgow mathematical journal PY - 2001 SP - 383 EP - 398 VL - 43 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089501030026/ DO - 10.1017/S0017089501030026 ID - 10_1017_S0017089501030026 ER -
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