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arXiv · 2011.05975

Small extensions of abelian ordered groups

Enric Nart
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Abstract

Let $\Gamma$ be a totally ordered group. We use Hahn's embedding theorem to construct a totally ordered set $\Gamma\subset \Gamma_{\operatorname{sme}}$ which classifies small extensions of $\Gamma$. This small-extensions closure $\Gamma_{\operatorname{sme}}$ is complete and plays a crucial role in the description of equivalence classes of valuations on the polynomial ring $K[x]$ over a field $K$.

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Enric Nart. 2020-11-02. Small extensions of abelian ordered groups. https://arxiv.org/abs/2011.05975

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