Let A be a right noetherian algebra over a field k. If the base field extension A ⊗_kK remains right noetherian for all extension fields K of k, then A is called stably right noetherian over k. We develop an inductive method to show that certain algebras of finite Gelfand-Kirillov dimension are stably noetherian, using critical composition series. We use this to characterize which algebras satisfying a polynomial identity are stably noetherian. The method also applies to many \(\mathbb {N}\)-graded rings of finite global dimension; in particular, we see that a noetherian Artin-Schelter regular algebra must be stably noetherian. In addition, we study more general variations of the stably noetherian property where the field extensions are restricted to those of a certain type, for instance purely transcendental extensions.

设A为在字段k上的右Noether代数。如果基本字段扩展甲⊗ _ķ ķ保持右诺特所有扩展字段ķ的ķ，然后甲称为稳定右诺特超过ķ。我们开发了一种归纳法，以证明使用临界成分级数的有限Gelfand-Kirillov维数的某些代数是稳定的noetherian。我们用它来表征满足多项式恒等式的代数稳定地为noetherian。该方法也适用于许多\（\ mathbb {N} \）有限全局尺寸的分级环；特别是，我们看到Noetherian Artin-Schelter正则代数必须稳定地为noetherian。另外，我们研究了稳定的noetherian属性的更一般的变化，其中场扩展仅限于某种类型的扩展，例如纯粹的先验扩展。