论文标题
小的阿贝尔有序小组的较小扩展
Small extensions of abelian ordered groups
论文作者
论文摘要
让$γ$成为一个完全有序的组。我们使用Hahn的嵌入定理来构造一个完全有序的集合$γ\ subsetγ_ {\ pereratatorName {sme}} $，该$ cans {sme}} $，该$分类为$γ$。这种小扩展封闭$γ_ {\ permatoratorname {sme}} $是完整的，并且在field $ k $上的多项式环$ k [x] $上的等价估价类别的描述中起着至关重要的作用。
Let $Γ$ be a totally ordered group. We use Hahn's embedding theorem to construct a totally ordered set $Γ\subset Γ_{\operatorname{sme}}$ which classifies small extensions of $Γ$. This small-extensions closure $Γ_{\operatorname{sme}}$ is complete and plays a crucial role in the description of equivalence classes of valuations on the polynomial ring $K[x]$ over a field $K$.
