It is a well-known result of Auslander and Reiten that contravariant finiteness of the class P∞
fin (of finitely generated modules of finite projective dimension) over an Artin algebra is a …

The famous finitistic dimension conjecture says that the supremum of the finite projective
dimensions of finitely generated modules over a given artin algebra is always finite. This …

Let A be an Artin algebra and e an idempotent element in A. In this paper, we use co-
homological conditions on A to control the finitistic dimension of eAe. Such a consideration …

Let $ A $ be an Artin algebra, $ M $ be a Gorenstein projective $ A $-module and $ B= $ End
$ _A M $, then $ M $ is a $ A $-$ B $-bimodule. We use the restricted flat dimension of …

We prove that the finitistic dimension conjecture, the Gorenstein Symmetry Conjecture, the
Wakamatsu-tilting conjecture and the generalized Nakayama conjecture hold for artin …

The famous finitistic dimension conjecture says that every finite-dimensional 𝕂-algebra over
a field 𝕂 should have finite finitistic dimension. This conjecture is equivalent to the following …

In this paper, we study the finitistic dimensions of artin algebras by establishing a
relationship between the global dimensions of the given algebras, on the one hand, and the …

We introduce the notion of relative hereditary Artin algebras, as a generalization of algebras
with representation dimension at most 3. We prove the following results.(1) The relative …

We investigate the relations between finitistic dimensions and restricted flat dimensions
(introduced by Foxby [LW Christensen, H.-B. Foxby, A. Frankild, Restricted homological …

Let R be a finite dimensional k-algebra over an algebraically closed field k and modR be the
category of all finitely generated left R-modules. For a given full subcategory X of modR, we …