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The structure of algebras admitting well agreeing near weights

Carlos Munuera·Fernando Torres
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Abstract

We characterize algebras admitting two well agreeing near weights $ρ$ and $σ$. 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 $ρ$ and $σ$ 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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Carlos Munuera, Fernando Torres. 2006-05-11. The structure of algebras admitting well agreeing near weights. https://arxiv.org/abs/math/0605306

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