We study the behavior of modules of $m$-integrable derivations of a commutative finitely generated algebra in the sense of Hasse-Schmidt under base change. We focus on the case of separable ring extensions over a field of positive characteristic and on the case where the extension is a polynomial ring in an arbitrary number of variables.

中文翻译：

---

基变下Hasse-Schmidt意义上的m-可积导数模的行为

我们研究了 Hasse-Schmidt 意义上的可交换有限生成代数的 $m$-可积导数的模在基数变化下的行为。我们专注于可分离环扩展在正特性域上的情况以及扩展是任意数量变量中的多项式环的情况。