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

Essentially finite generation of valuation rings in terms of classical invariants