Valuation Extensions of Filtered and Graded Algebras

Details Valuation Extensions of Filtered and Graded Algebras Valuation Extensions of Filtered and Graded Algebras

2005-09-23

arxiv.org/abs/math/0509542v1

Mathematics

Rings and Algebras

12 pages

Scientific paper

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 an associated graded ring having a domain for its reduction.

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