We introduce the class of double tilted algebras, containing the class of tilted algebras and
prove various characterizations. In particular, we show that the class of double tilted …

Let R be a left and right Noetherian ring. In this paper, we prove that any Gorenstein
transpose of a finitely generated R-module is exactly an Auslander transpose. As …

Generic modules were introduced by Crawley-Boevey in order to provide a better
understanding of finite-dimensional algebras of tame representation type. In fact he has …

In this dissertation, let B be a triangulated category and let D be an extension-closed
subcategory of B. First, we give some new characterizations of an Auslander-Reiten triangle …

Let A be a connected hereditary artin algebra. We show that the set of functorially finite
torsion classes of A-modules is a lattice if and only if A is either representation-finite (thus a …

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 …

We will study the relationship of quite different objects in the theory of artin algebras, namely
Auslander-regular rings of global dimension two, torsion theories, $\tau $-categories and …

We investigate (existence of) Auslander–Reiten triangles in a triangulated category in
connection with torsion pairs, existence of Serre functors, representability of homological …

Let be an Artin algebra over a commutative Artin ring R and let mod be the category of
finitely generated left-modules. For a module M∈ mod we denote by pd M the projective …

Tilting theory is known as a powerful tool for studying representation theory of artin algebras.
Though there are no non-trivial tilting modules over sel: finjective algebras, we have a way …