Global homological dimension of multifiltered rings and quantized enveloping algebras (Q1972411)

The authors consider multifiltered rings (by the free Abelian semigroup \(\mathbb{N}^p\) with a certain admissible order), the associated graded ring and the transfer of certain properties from one to the other. The connection between multifiltered and graded modules is specialized to free and projective modules. As a consequence it is proved that the projective dimension of a multifiltered module is bounded by the projective dimension of the associated graded module. Similar bounds are given for Krull and flat dimensions. The results are applied to several quantum groups.