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- W2897764602 abstract "Let $A$ be a right noetherian algebra over a field $k$. If the base field extension $A otimes_k K$ 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 $mathbb{N}$-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." @default.
- W2897764602 created "2018-10-26" @default.
- W2897764602 creator A5000721810 @default.
- W2897764602 date "2018-10-13" @default.
- W2897764602 modified "2023-09-27" @default.
- W2897764602 title "Stably Noetherian Algebras of Polynomial Growth" @default.
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- W2897764602 hasPublicationYear "2018" @default.
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