GROBNER BASES OF CHARACTERISTIC IDEALS OF LRS OVER UFD

Let R be a unique factorization domain (UFD). A method of Grobner base s and localization in commutative algebra is applied to compute and an alyze the characteristic ideals of semi-infinite linear recurring sequ ences (Irs), infinite linear recurring sequences (LRS), and finite Irs over UFD. The canonical form of a minimal Grobner basis of the homoge neous characteristic ideal is described for a finite segment of an Irs , from which a precise relation between every step in the classical Be rlekamp-Massey algorithm and every member of the Grobner basis is deri ved.