International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 327-334

Invariance of recurrence sequences under a galois group

Hassan Al-Zaid and Surjeet Singh

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 F be a Galois field of order q, k a fixed positive integer and R=Fk×k[D] where D is an indeterminate. Let L be a field extension of F of degree k. We identify Lf with fk×1 via a fixed normal basis B of L over F. The F-vector space Γk(F)(=Γ(L)) of all sequences over Fk×1 is a left R-module. For any regular f(D)R, Ωk(f(D))={SΓk(F):f(D)S=0} is a finite F[D]-module whose members are ultimately periodic sequences. The question of invariance of a Ωk(f(D)) under the Galois group G of L over F is investigated.