There exists a hierachy of homological conjectures for finitely generated modules over an
Artin algebra A. The generalized Nakayama conjecture for example states that each …

We investigate the (separated) monomorphism category $\operatorname
{mono}(Q,\Lambda) $ of a quiver $ Q $ over an Artin algebra $\Lambda $. We construct an …

We consider Λ Λ an artin algebra and n ≥ 2 n≥ 2. We study how to compute the left and
right degrees of irreducible morphisms between complexes in a generalized standard …

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 …

These notes are devoted to a single invariant, the Gabriel-Roiter measure of finite length
modules: this invariant was introduced by Gabriel (under the name 'Roiter measure') in 1972 …

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Let be a component of the Auslander-Reiten quiver of an Artin algebra containing projective
and injective modules. Assume that the length of any path from an injective in to a projective …

Using a notion of distance between indecomposable modules we deduce new
characterizations of laura algebras and quasi-directed Auslander-Reiten components …

We study the degree of irreducible morphisms in generalized standard convex components
of the Auslander–Reiten quiver of an artin algebra with the property that paths with the same …