Reduced Grobner Bases, Free Difference-Differential Modules and Difference-Differential Dimension Polynomials

摘要

We define a special type of reduction in a free left module over a ring of difference- differential operators and use the idea of the Grobner basis method to develop a tech- nique that allows us to determine the Hilbert function of a finitely generated difference- differential module equipped with the natural double filtration. The results obtained are applied to the study of difference-differential field extensions and systems of difference- differential equations.