Graded Extensions in a Skew Laurent Polynomial Ring*

摘要

Let V be a total valuation ring of a division ring K with an automorphism σ and let R be a Gauss extension of V in K(X, σ). Then A = R ∏ K[X, X(~1);σ] is a graded extension of V in K[X, X(~1); σ], the skew Laurent polynomial ring, and A(_jg)(A), the localization of the graded Jacobson radical J_g(A) of A, is equal to R. Let A be a graded extension of V in K[X,X(~1); σ]. Graded extensions contained in A and graded extensions containing A will be studied in this paper.