We consider filtered or graded algebras A over a field K. Assume that
there is a discrete valuation Ovβ of K with mvβ its maximal ideal and
kvβ:=Ovβ/mvβ its residue field. Let Ξ be Ovβ-order such that
ΞK=A and ΞΛ:=kvββOvββΞ the
Ξ-reduction of A at the place Kβkvβ. Using the filtration
of A induced by Ξ we shall prove that for certain algebras A their
properties are related to ΞΛ.Comment: 17 page