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 …

In Section l we recall some of the features of Frobenius categories in the setup we need. In
particular, we give an Interpretation of the triangles in a Frobenius category in term of exact …

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 …

Let A be an Artin algebra and T∙ a two-term tilting complex of A. We determine when T∙
induces a TTF theory for the module category over A. Next, we assume A is self-injective …

Let $\Lambda $ be an artin algebra or, more generally, a locally bounded associative
algebra, and $\mathcal {S}(\Lambda) $ the category of all embeddings $(A\subseteq B) …

We study Auslander-Reiten theory in proper abelian subcategories of triangulated
categories with a Serre functor. To initiate this, we use approximations of a Serre functor to …

Let A be a small abelian category. For a closed subbifunctor F of Ext A 1 (−,−), Buan has
generalized the construction of Verdier's quotient category to get a relative derived category …

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 …

Let A be an artin algebra and mod A the category of finitely generated A-modules. If X is in
mod/i let (, X) denote the contravariant functor Hom (, X) from mod A to abelian groups. If F is …

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 …