A theorem of Serre for the ring of twisted formal series

Abstract

In this paper we prove that if R is a left Noetherian and left regular ring such that all finitely generated projective left R-modules are stably free, then the same is true for the completion R[[x;\sigma,\delta]] of any Ore extension R[x;\sigma,\delta] of R. Additionally assumes certain natural conditions for \sigma and \delta for ensure that this completion are good defined. The proof compares the Grothendieck groups K_{0} of R and S using some results find in [3], [6], [7] and [9].