We consider artin algebras with duality functor D. We consider left modules (usually, we call
them just modules) as well as right modules. Maps will act on the opposite side of the …

Degrees of irreducible morphisms in coherent almost cyclic Auslander–Reiten components -
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Let Λ be an artin algebra, and denote by mod Λ the category of finitely generated Λ-
modules. All modules we consider are finitely generated. We recall from [6] that a nonsplit …

Let A be an Artin algebra. The A-modules which we consider are always left modules of
finite length. If X, Y, Z are A-modules, the composition of maps f: X~ Y and g: Y~ Z is denoted …

We describe the structure of semi‐regular Auslander–Reiten components of artin algebras
without external short paths in the module category. As an application, we give a complete …

Let Λ be an artin algebra. The aim of this paper is to outline a strong relationship between
the Gabriel–Roiter inclusions and the Auslander–Reiten theory. If X is a Gabriel–Roiter …

We consider functorially finite subcategories in module categories over Artin algebras. One
main result provides a method, in the setup of bounded derived categories, to compute …

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 …

The aim of these notes is to report some new developments on the problem of describing all
possible shapes of the connected components of the Auslander-Reiten quiver ΓA of an artin …

Let A be an artin algebra over a commutative artin ring R and ind A the category of
indecomposable finitely generated right A-modules. Denote L _A to be the full subcategory …