  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.
