On the dimension theory of skew power series rings

Abstract

The first purpose of this paper is to set up a general notion of skew power series rings S over a coefficient ring R, which are then studied by filtered ring techniques. The second subject consists of investigating the class of S-modules which are finitely generated as R-module. In the case that S and R are Auslander regular we show in particular that the codimension of M as S-module is one higher than the codimension of M as R-module. Furthermore its class in the Grothendieck group of S-modules of codimension at most one less vanishes, which is in the spirit of the Gersten conjecture for commutative regular local rings. Finally we apply these results to Iwasawa algebras of p-adic Lie groups.