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 introduce the concept of maximal (n− 1)-orthogonal subcategories over Artin algebras
and orders, and develop (n+ 1)-dimensional Auslander–Reiten theory on them. We give the …

We shall sketch the existence of Auslander-Reiten sequences for Artin algebras and for
orders, which is based on a common construction, pointing out where exactly the cases of …

Bazzoni had given a simple characterization of infinitely generated n-tilting modules.
Though her method is even inapplicable to classical n-tilting modules over Artin algebras …

In the category of finitely generated modules over an artinian ring, we classify all the abelian
exact subcategories closed under predecessors or, equivalently, all the split torsion pairs …

First, we show that a compact object C in a triangulated category, which satisfies suitable
conditions, induces a t-structure. Second, in an abelian category we show that a complex P …

Let k be a commutative artinian ring and 𝒜 a small Ext-finite Krull–Schmidt n-abelian k-
category with enough projectives and injectives. We introduce two full subcategories 𝒜 r and …

In this paper, we introduce and study a class of algebras which we call ada algebras. An
artin algebra is ada if every indecomposable projective and every indecomposable injective …

0-> A-> B-> C-> 0 is called an almost split sequence if a) it is not splitable, b) A and C are
indecomposable A-modules and c) if f: X-> C is not a splitable epimorphism, then there is an …

We introduce a relative tilting theory in abelian categories and show that this work offers a
unified framework of different previous notions of tilting, ranging from Auslander-Solberg …