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Peizhong Lu 《Applicable Algebra in Engineering, Communication and Computing》2000,11(2):141-156
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 Gr?bner bases. Our result
is a solution of Nechaevs Open Problem suggested in [11].
Received: July 10, 1999; revised version: February 14, 2000 相似文献