… Maps are written on the right. … Degrees of irreducible maps In this section we define left
degree and right degree for an irreducible map. We extend a technique used by Bongartz in [8] …

… To be able to compare the AR-quivers for R and R, we need more information about
irreducible maps to R (and dually irreducible maps from w). We have the following: …

… split map B + C, and for A indecomposable injective there is a minimal left almost split map A
… is a finite set of indecomposable modules closed under irreducible maps, then %? consists …

… split map B→ C, and for A indecomposable injective there is a minimal left almost split map
A… a finite set of indecomposable modules closed under irreducible maps, then consists of all …

… (X,Y)O' Assume now that we have a nonzero degree zero map g: Y + … By considering
the minimal left almost split map h: Y + E … we can find an irreducible map f …

… classical Auslander-Reiten theory we can define irreducible maps, minimal maps, left almost
split maps and right almost split maps… than in the case of Artin algebras for irreducible maps: …

… In Section 2, we present some background material, including the properties of irreducible
morphisms and the Auslander-Reiten theory for triangulated categories. In Section 3, we …

… In the third section irreducible maps of complexes in Comp−,b(P) that end in an
indecomposable contractible complex are analyzed. We show that these irreducible maps start in a …

… as a generalization of an irreducible element in a ring. The Auslander–Reiten quiver turns
out to … , that hyperbolic maps form an open dense subset in the space of degree d rational …

… In Chapter 3 we introduce degrees of irreducible morphisms and use this notion to prove …
For convenience, we say that a right almost split morphism that maps to a module Y is a right …