Abstract.
Let R be a local Artin principal ideal ring, R[x] the polynomial ring over R with indeterminate x. Let π be an element of R such that <π> is the unique maximal ideal of R. Let I be a zero-dimensional ideal of R[x], and the radical ideal of I. In this paper we show that I is the annihilating ideal of a linear recurring sequence over R if and only if I satisfies the following formula
The two sides of the formula can be feasibly computed by some typical algorithms from the theory of Gröbner bases. Our result is a solution of Nechaevs Open Problem suggested in [11].
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: July 10, 1999; revised version: February 14, 2000
Rights and permissions
About this article
Cite this article
Lu, P. A Criterion for Annihilating Ideals of Linear Recurring Sequences over Galois Rings. AAECC 11, 141–156 (2000). https://doi.org/10.1007/s002000000040
Issue Date:
DOI: https://doi.org/10.1007/s002000000040