The Structure of Algebras Admitting Well Agreeing Near Weights

We characterize algebras admitting two well agreeing near weights $\rho$ and $\sigma$. We show that such an algebra $R$ is an integral domain whose quotient field $\K$ is an algebraic function field of one variable. It contains two places $P, Q\in {\mathbb P}(\K)$ such that $\rho$ and $\sigma$ are derived from the valuations associated to $P$ and $Q$. Furthermore$\bar R=\cap_{S\in \bP(\K)\setminus\{P,Q\}} \cO_S$.