Let be a total valuation ring of a division ring with an automorphism and let be a graded extension of in , the skew Laurent polynomial ring. We classify by distinguishing four different types based on the properties of and . A complete description of for all is given in the case where is a finitely generated left -ideal.
Hidetoshi MARUBAYASHI. Guangming XIE. "A classification of graded extensions in a skew Laurent polynomial ring." J. Math. Soc. Japan 60 (2) 423 - 443, April, 2008. https://doi.org/10.2969/jmsj/06020423