Gelfand-Kirillov dimensions of differential difference modules via Gr?bner bases

摘要

Introduction. Differential-difference algebras were defined by Mansfield and Szanto in [5], which arose from the calculation of symmetries of discrete systems (c.f., [2]). Mansfield and Szanto developed the Gr?bner basis theory of differential difference algebras over a field by using a special kind of left admissible orderings (which they called differential difference orderings). We generalize the main results of [5] to any left admissible ordering, and apply the generalized results to compute the Gelfand-Kirillov dimensions of cyclic differential difference modules.