TY - RPRT
A1 - Hachenberger, Dirk
T1 - On Completely Free Elements in Finite Fields
N2 - We show that the different module structures of GF(\(q^m\)) arising from the intermediate fields of GF(\(q^m\))and GF(q) can be studied simultaneously with the help of some basic properties of cyclotomic polynomials. We use this ideas to give a detailed and constructive proof of the most difficult part of a Theorem of D. Blessenohl and K. Johnsen (1986), i.e., the existence of elements v in GF(\(q^m\)) over GF(q) which generate normal bases over any intermediate field of GF(\(q^m\)) and GF(q), provided that m is a prime power. Such elements are called completely free in GF(\(q^m\)) over GF(q). We develop a recursive formula for the number of completely free elements in GF(\(q^m\)) over GF(q) in the case where m is a prime power. Some of the results can be generalized to finite cyclic Galois extensions
over arbitrary fields.
T3 - Preprints (rote Reihe) des Fachbereich Mathematik - 232
Y1 - 1992
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5042
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-50424
ER -