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

Let A be an Artin algebra and e be an idempotent element of A. We prove that if A has
representation dimension at most three, then the finitistic dimension of eAe is finite, and …

An extension of algebras is a homomorphism of algebras preserving identities. We use
extensions of algebras to study the finitistic dimension conjecture over Artin algebras. Let f …

We study Auslander's representation dimension of Artin algebras, which is by definition the
minimal projective dimension of coherent functors on modules which are both generators …

We use the class of representation-finite algebras to investigate the finitistic dimension
conjecture. In this way we obtain a large class of algebras for which the finitistic dimension …

FINITENESS OF REPRESENTATION DIMENSION M. Auslander introduced a concept of
representation dimension of artin algebras in [A], w Page 1 PROCEEDINGS OF THE …

Auslander has shown that an algebra is of finite representation type, that is, it admits only
finitely many indecomposable modules up to isomorphism, if and only if its representation …

In this note, we prove that if $\Lambda $ is an Artin algebra with a simple module $ S $ of
finite projective dimension, then the finiteness of the finitistic dimension of $\Lambda …

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 …