  The aim of this article is to introduce standard bases of ideals in
polynomial rings with respect to a class of orderings which are not necessarily
semigroup orderings. Our approach generalises the concept of standard bases
with respect to semigroup orderings described by Graebe and Greuel/Pfister. To
compute these standard bases we give a slightly modified version of the
Buchberger algorithm. The orderings we consider are refinements of certain
filtrations. In the local case these filtrations are Newton filtrations. For a
zero dimensional ideal, an algorithm converting standard bases with respect to
local orderings is given. As an application, we show how to compute the
spectrum of an isolated complex hypersurface singularity $f:(C^n,0)\to(C,0)$
with nondegenerate principal part.
