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 …

From certain triangle functors, called nonnegative functors, between the bounded derived
categories of abelian categories with enough projective objects, we introduce their stable …

Auslander-Reiten conjecture, which says that an Artin algebra does not have any non-
projective generator with vanishing self-extensions in all positive degrees, is shown to be …

We study derived invariance through syzygy complexes. In particular, we prove that syzygy-
finite algebras and Igusa--Todorov algebras are invariant under derived equivalences …

We introduce the finitistic extension degree of a ring and investigate rings for which it is
finite. The Auslander–Reiten Conjecture is proved for rings of finite finitistic extension …

In this paper, we introduce a class of algebras called Φ-Cohen–Macaulay Auslander–
Yoneda algebras with Φ an admissible set of ℕ, and construct derived equivalences …

Full article: Generalized Auslander-Reiten Conjecture and Derived Equivalences Skip to Main
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Assume that whose ext-algebra is finite dimensional. This gives a complete classification of
weakly symmetric indecomposable algebras which have a nonprojective module whose ext …