Localizations and completions of skew power series rings

Abstract

This paper is a natural continuation of the study of skew power series rings $A=R[[t;\sigma,\delta]]$ initiated in an earlier work. We construct skew Laurent series rings $B$ and show the existence of some canonical Ore sets $S$ for the skew power series rings $A$ such that a certain completion of the localization $A_S$ is isomorphic to $B.$ This is applied to certain Iwasawa algebras. Finally we introduce subrings of overconvergent skew Laurent series rings.