Let V be a total valuation ring of a division ring K with an automorphism s and let R be a Gauss extension of V in �Then � �is a graded extension of V in �the skew Laurent polynomial ring, and �the localization of the graded Jacobson radical �of A, is equal to R. In this paper, we give a complete description of the residue skew fields of Gauss extensions.

graded extension, total valuation ring, residue skew field, Gauss extension.