  We introduce the semiring of values $\Gamma$ with respect to the tropical
operations associated to an algebroid curve. As a set, $\Gamma$ determines and
is determined by the well known semigroup of values $S$ and we prove that
$\Gamma$ is always finitely generated in contrast to $S$. In particular, for a
plane curve, we present a straightforward way to obtain $\Gamma$ in terms of
the semiring of each branch of the curve and the mutual intersection
multiplicity of its branches. In the analytical case, this allows us to connect
directly the results of Zariski and Waldi that characterize the topological
type of the curve.
