A classification of graded extensions in a skew Laurent polynomial ring. II. (Q1046437)

Suppose that \(K\) is a division ring with an automorphism \(\sigma\) and \(V\) a valuation of \(K\). Let \(A=A_i[X^{\pm 1};\sigma]\) be a skew polynomial subring in the skew Laurent polynomial ring \(K[X^{\pm 1};\sigma]\) such that any monomial or its inverse belong to \(A\). The aim of the paper is to classify the ring \(A\) under the assumption that \(A_0=V\). For part I cf. the authors, ibid. 60, No. 2, 423-443 (2008; Zbl 1147.16030).