LAUSR

Let A be a right noetherian algebra over a field k . If the base field extension A ⊗ k K 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 ℕ $\mathbb {N}$ -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.