A classification of graded extensions in a skew Laurent polynomial ring

Abstract

Let V be a total valuation ring of a division ring K with an automorphism σ and let A = $\oplus$_{i ∈ Z} A_iXⁱ be a graded extension of V in K[X,X^-1;σ], the skew Laurent polynomial ring. We classify A by distinguishing four different types based on the properties of A₁ and A_-1. A complete description of A_i for all i ∈ Z is given in the case where A₁ is a finitely generated left O_l(A₁)-ideal.