Valuation Extensions of Filtered and Graded Algebras

  title={Valuation Extensions of Filtered and Graded Algebras},
  author={C. BAETICA and Freddy Van Oystaeyen},
In this note we relate the valuations of the algebras appearing in the non-commutative geometry of quantized algebras to properties of sub-lattices in some vector spaces. We consider the case of algebras with PBW -bases and prove that under some mild assumptions the valuations of the ground field extend to a non-commutative valuation. Later we introduce the notion of F -reductor and graded reductor and reduce the problem of finding an extending non-commutative valuation to finding a reductor in… CONTINUE READING