Skew-power series over prime rings (joint with William Woods)

Let R be a ring carrying an automorphism \sigma and a \sigma-derivation \delta. We are interested in the skew-power series ring R[[x;\sigma,\delta]], in the cases when it is well defined. Specifically, we want to prove analogues of properties of the well studied skew-polynomial ring R[x;\sigma,\delta] to the skew power series case. We will focus on the question: if R is a prime, Noetherian ring, is R[[x;\sigma,\delta]] also prime? We will partially answer this question in the case where R carries an appropriate topology such that (\sigma,\delta) are continuous, focusing particularly on the case where \delta=\sigma-1.

This talk is part of the Birmingham Algebra Seminar series.