Summary: On Linear Difference Equations over Rings and
Jawad Y. Abuhlail
P.O.Box 14, Birzeit - Palestine
In this note we develop a coalgebraic approach to the study of solutions of linear
difference equations over modules and rings. Some known results about linearly recur-
sive sequences over base fields are generalized to linearly (bi)recursive (bi)sequences
of modules over arbitrary commutative ground rings.
Although the theory of linear difference equations over base fields is well understood, the
theory over arbitrary ground rings and modules is still under development. It is becoming
more interesting and is gaining increasingly special importance mainly because of recent
applications in coding theory and cryptography (e.g. [HN99], [KKMMN99]).
In a series of papers E. Taft et al. (e.g. [PT80], [LT90], [Taf95]) developed a coalgebraic
aspect to the study of linearly recursive sequences over fields. Moreover L. Gršunenfelder
et al. studied in ([GO93], [GK97]) the linearly recursive sequences over finite dimensional