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 …

Text of a (pre-dinner) lecture at the Bielefeld workshop" Discrete Categories in
Representation Theory", April 20-21, 2018. This workshop was organized in order to …

We give an alternative proof to the fact that, if the square of the infinite radical of the module
category of an Artin algebra is equal to zero, then the algebra is of finite type by making use …

For the module category of an Artin algebra, we generalize the notion of torsion pairs to
ideal torsion pairs. Instead of full subcategories of modules, ideals of morphisms of the …

We introduce syzygies for derived categories and study their properties. Using these, we
prove the derived invariance of the following classes of artin algebras:(1) syzygy-finite …

We characterize the finiteness of the representation type of an artin algebra in terms of the
behavior of the projective covers and the injective envelopes of the simple modules with …

For an exact category E, we study the Butler's condition “AR= Ex”: the relation of the
Grothendieck group of E is generated by Auslander-Reiten conflations. Under some …

We know that the model theory of modules leads to a way of obtaining definable categories
of modules over a ring R as the kernels of certain functors (RM od) op→ A b rather than of …

Using a relative version of Auslander's formula, we show that bounded derived category of
every artin algebra admits a categorical resolution. This, in particular, implies that bounded …

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 …