The extended center of a skew power series ring

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Abstract
For a prime ring R with σ ∊ Aut(R), we examine the extended center of the skew power series ring R[[x;σ]]. We prove the extended center of R[[x;σ]] is isomorphic to: (1) Cσ if no power of σ is X-inner where Cσ is the fixed field of a acting on the extended center C of R (2) Cσ((vx')) (Laurent series) if some positive power of a is X-inner and R is closed prime. In this case I is the least positive integer such that a1 is X-inner with σ1= inn(v). We provide an example showing this result fails if R is not closed prime.

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