2018/10/13 by Rogalski, Daniel
#16P90 #16R20 #16S38 #16W50. Secondary:16E65 #FOS: Mathematics #Primary: 16P40 #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1810.05769
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-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.