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- W2951431430 abstract "Auslander conjectured that every Artin algebra satisfies a certain condition on vanishing of cohomology of finitely generated modules. The failure of this conjecture - by a 2003 counterexample due to Jorgensen and Sega - motivates the consideration of the class of rings that do satisfy Auslander's condition. We call them AC rings and show that an AC Artin algebra that is left-Gorenstein is also right-Gorenstein. Furthermore, the Auslander-Reiten Conjecture is proved for AC rings, and Auslander's G-dimension is shown to be functorial for AC rings that are commutative or have a dualizing complex." @default.
- W2951431430 created "2019-06-27" @default.
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- W2951431430 date "2008-01-02" @default.
- W2951431430 modified "2023-09-26" @default.
- W2951431430 title "Algebras that satisfy Auslander's condition on vanishing of cohomology" @default.
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