A classification of graded extensions in a skew Laurent polynomial ring, II

Abstract

Let V be a total valuation ring of a division ring K with an automorphism σ and let A=⊕_i∈ZA_iXⁱ be a graded extension of V in K[X,X⁻¹;σ], the skew Laurent polynomial ring. We classify A by distinguishing three different types based on the properties of A₁ and A₋₁, and a complete description of A_i for all i∈Z is given in the case where A₁ is not a finitely generated left O_l(A₁)-ideal.