  The main goal of this paper is to study some properties of an extension of
valuations from classical invariants. More specifically, we consider a valued
field $(K,\nu)$ and an extension $\omega$ of $\nu$ to a finite extension $L$ of
$K$. Then we study when the valuation ring of $\omega$ is essentially finitely
generated over the valuation ring of $\nu$. We present a necessary condition in
terms of classic invariants of the extension by Hagen Knaf and show that in
some particular cases, this condition is also sufficient. We also study when
the corresponding extension of graded algebras is finitely generated. For this
problem we present an equivalent condition (which is weaker than the one for
the finite generation of the valuation rings).
