The structure of algebras admitting well agreeing near weights

Details The structure of algebras admitting well agreeing near weights The structure of algebras admitting well agreeing near weights

2006-05-11

arxiv.org/abs/math/0605306v1

Mathematics

Algebraic Geometry

10 pages

Scientific paper

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 $\mathbf K$ is an algebraic function field of one variable. It contains two places $p, Q\in {\mathbb P}(\mathbf K)$ such that $\rho$ and $\sigma$ are derived from the valuations associated to $P$ and $Q$. Furthermore $\bar R= \cap_{S\in\{\mathbb P}(\mathbf F)\setminus\{P,Q\}}{\mathcal O}_S$.

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