Let A be an artin algebra. An A-module M will be said to be semi-Gorenstein-projective
provided that Ext i (M, A)= 0 for all i≥ 1. All Gorenstein-projective modules are semi …

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 …

We consider the question of whether the injective modules generate the unbounded derived
category of a ring as a triangulated category with arbitrary coproducts. We give an example …

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 …

We give counterexamples to the following conjecture of Auslander: given a finitely
generated module M over an Artin algebra Λ, there exists a positive integer nM such that for …

We construct a local Cohen–Macaulay ring R with a prime ideal p∈ Spec (R) such that R
satisfies the uniform Auslander condition (UAC), but the localization R p does not satisfy …

The notion of Igusa–Todorov algebras is introduced in connection with the (little) finitistic
dimension conjecture, and the conjecture is proved for those algebras. Such algebras …

Left–right symmetry of finite finitistic dimension - Cummings - 2024 - Bulletin of the London
Mathematical Society - Wiley Online Library Skip to Article Content Skip to Article Information …

The main objective of this paper is to study the relative derived categories from various
points of view. Let A be an abelian category and C be a contravariantly finite subcategory of …

In this paper, we develop new ideas regarding the finitistic dimension conjecture, or the
findim conjecture for short. Specifically, we improve upon the delooping level by introducing …