Auslander-Reiten conjecture and Auslander-Reiten duality

Details Auslander-Reiten conjecture and Auslander-Reiten duality Auslander-Reiten conjecture and Auslander-Reiten duality

2011-12-28

arxiv.org/abs/1112.6201v1

Mathematics

Commutative Algebra

14 pages

Scientific paper

Motivated by a result of Araya, we extend the Auslander-Reiten duality
theorem to Cohen-Macaulay local rings. We also study the Auslander-Reiten
conjecture, which is rooted in Nakayama's work on finite dimensional algebras.
One of our results detects a certain condition that forces the conjecture to
hold over local rings of positive depth.

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