We define the global cohomological range for artin algebras, and define the derived
bounded algebras to be the algebras with finite global cohomological range, then we prove …

This paper aims to initiate a study of the representation theory of representation-finite artin
algebras in terms of the nilpotency of the radical of their module category. Firstly, we shall …

The importance of the representation finite Artin algebras for the whole representation theory
of Artin algebras is well understood and there is much literature on the subject (see [1, 6 …

Co-Gorenstein algebras were introduced by Beligiannis in [A. Beligiannis, The homological
theory of contravariantly finite subcategories: Auslander–Buchweitz contexts, Gorenstein …

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 …

The Krull-Gabriel Dimension of Cycle-Finite Artin Algebras Page 1 Algebr Represent Theor (2016)
19:215–233 DOI 10.1007/s10468-015-9571-6 The Krull-Gabriel Dimension of Cycle-Finite Artin …

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 …

Co-Gorenstein algebras were introduced by A. Beligiannis in\cite {B}. In\cite {KM}, the
authors propose the following conjecture (Co-GC): if $\Omega^ n (\mod A) $ is extension …

One of the first remarkable results in the representation theory of artin algebras, due to
Auslander and Ringel-Tachikawa, is the characterisation of when an artin algebra is …