International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 327-334
Invariance of recurrence sequences under a galois group
Department of Mathematics, Kuwait University, P O Box 5969, Safat 13060, Kuwait
Received 25 October 1993; Revised 9 May 1995
Copyright © 1996 Hassan Al-Zaid and Surjeet Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a Galois field of order , a fixed positive integer and
where is an indeterminate. Let be a field extension of of degree . We identify with via
a fixed normal basis of over . The -vector space of all sequences over is
a left -module. For any regular , is a finite -module whose members are ultimately periodic sequences. The question of invariance of a
under the Galois group of over is investigated.