LINEAR RECURRING SEQUENCES OVER NONCOMMUTATIVE RINGS

Abstract

Contrary to the commutative case, the set of linear recurring sequences with values in a module over a noncommutative ring is no more a module for the usual operations. We show the stability of these operations when the ring is a matrix ring or a division ring. In the case of a finite dimensional division ring over its center, we give an algorithm for the determination of a recurrence relation for the sum of two linear recurring sequences.