论文标题
整数的商圈从度量的角度
Quotient rings of integers from a metric point of view
论文作者
论文摘要
Gromov-Hausdorff收敛的理论应用于整数的商环序列。它显示了极限环（字段）作为度量标准环序列的Gromov-Hausdorff限制的存在。讨论了这些结构与真实的$ \ mathbb {r} $的关系，这表明它们在$ \ mathbb {r} $中密集，但至少在$ \ \ m imak $ {q math $ n meth $中，它们无法与真实字段或理性字段$ \ mathbb {q} $相关。结构。还表明，极限环可以赋予订单关系。
The theory of Gromov-Hausdorff convergence is applied to sequences of quotient rings of integers. It is shown the existence of limit rings (fields) as the Gromov-Hausdorff limits of sequences of metric quotient rings. The relation of these constructions with the field of the reals $\mathbb{R}$ is discussed, showing that they are dense in $\mathbb{R}$ but that they cannot be identified with the real field or with the rational field $\mathbb{Q}$, at least when $\mathbb{R}$ and $\mathbb{Q}$ are endowed with the usual metric structures. It is also shown that the limit rings can be endowed with an order relation.
