Auslander–Reiten conjecture and Auslander–Reiten duality
O Celikbas, R Takahashi - Journal of Algebra, 2013 - Elsevier
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 …
Macaulay local rings. We also study the Auslander–Reiten conjecture, which is rooted in …
Stable functors of derived equivalences and Gorenstein projective modules
From certain triangle functors, called nonnegative functors, between the bounded derived
categories of abelian categories with enough projective objects, we introduce their stable …
categories of abelian categories with enough projective objects, we introduce their stable …
Singular equivalences and Auslander-Reiten conjecture
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 …
projective generator with vanishing self-extensions in all positive degrees, is shown to be …
Derived invariance by syzygy complexes
J Wei - … Proceedings of the Cambridge Philosophical Society, 2018 - cambridge.org
We study derived invariance through syzygy complexes. In particular, we prove that syzygy-
finite algebras and Igusa--Todorov algebras are invariant under derived equivalences …
finite algebras and Igusa--Todorov algebras are invariant under derived equivalences …
Finitistic extension degree
K Diveris - Algebras and Representation Theory, 2014 - Springer
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 …
finite. The Auslander–Reiten Conjecture is proved for rings of finite finitistic extension …
Derived equivalences for Φ-Cohen–Macaulay Auslander–Yoneda algebras
S Pan - Algebras and Representation Theory, 2014 - Springer
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 …
Yoneda algebras with Φ an admissible set of ℕ, and construct derived equivalences …
Generalized Auslander-Reiten conjecture and derived equivalences
S Pan - Communications in Algebra, 2013 - Taylor & Francis
Full article: Generalized Auslander-Reiten Conjecture and Derived Equivalences Skip to Main
Content Taylor and Francis Online homepage Browse Search Publish Login | Register Log in or …
Content Taylor and Francis Online homepage Browse Search Publish Login | Register Log in or …
Ext-finite modules for weakly symmetric algebras with radical cube zero
K Erdmann - Journal of the Australian Mathematical Society, 2017 - cambridge.org
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 …
weakly symmetric indecomposable algebras which have a nonprojective module whose ext …