标题： 不可分序列和可降性 显示英文标题

标题： Indivisible Sequences and Descendability

摘要： 我们引入不可分序列的概念，并证明对于任何不可分序列$\{S, \Psi: S \to R\}$，我们可以关联忠实平坦环映射$R \to R'$，这些映射不可下移。 作为推论，我们得到了第一个在$\aleph_{n-1}$-可数环之间的忠实平坦环映射，其下移指数为$n$，并且确实得到了在$\aleph_{\omega}$-可数环之间的忠实平坦环映射，该映射不可下移。 显示英文摘要

摘要： We introduce the notion of indivisible sequences and show that to any indivisible sequence $\{S, \Psi: S \to R\}$ we can associate faithfully flat ring maps $R \to R'$ that are not descendable. As a corollary, we obtain the first example of a faithfully flat ring map between $\aleph_{n-1}$-countable rings that has descendability exponent $n$, and indeed a faithfully flat ring map between $\aleph_{\omega}$-countable rings that is not descendable.