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 …

Using a relative version of Auslander's formula, we give a functorial approach to show that
the bounded derived category of every Artin algebra admits a categorical resolution. This, in …

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 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 …

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 …

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 …

ON CONTRAVARIANTLY FINITE SUBCATEGORIES Claus Michael Ringel Abstract. Let A be an
artin algebra. Let / 1, /2 be contravari- ant Page 1 ON CONTRAVARIANTLY FINITE …

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 …

We clarify the relation between the subcategory D hf b (A) of homological finite objects in D b
(A) and the subcategory K b (P) of perfect complexes in D b (A), by giving two classes of …

We study the global dimensions of the coherent functors over two categories that are linked
by a pair of adjoint functors. This idea is then exploited to compare the representation …