… constructed quite a long time ago by Auslander and Reiten, recently another one by Li and
… modules. If we use our labels, so that \(P(n) = I(n)\) is the unique indecomposable module …

… of the module category of a tame hereditary algebra obtained by using Auslander–Reiten
theory … We show that all preprojective modules lie in the take-off part (Theorem 4.4). A direct …

… that both modules X … module X , there exists an AuslanderReiten sequence starting
with X , and also dually, given an indecomposable non-projective Z , there is an Auslander-Reiten …

… Auslander-Reiten duality, ie there exist an equivalence functor τG : Gprj-Λ → Gprj-Λ such that
for any Gorenstein projective modules G … Kleinian singularities and preprojective algebras, …

… Auslander-Reiten sequence for A/I. Thus we may assume that A has a faithful indecomposable
module… Let T be a preprojective translation quiver with orbit graph OU); see [7]. A vertex x …

… In chapter 4 we consider the set Tp(Q) of basic pre-projective tilting modules and study its …
sequences and Auslander-Reiten quivers. In section 3 we review Auslander-Reiten theory …

… called a sincere preprojective component if there is a sincere indecomposable module M in
… Theorem Let P be a sincere preprojective component of the AuslanderReiten quiver of an …

… all preprojective modules. In particular, there are no non-trivial maps EIP(n, r) → EKP(n, r).
We want to determine the relative position of these modules in the Auslander-Reiten quiver Γ(…

… IT contains no injective module in mod B and , preserves monomorphisms in 3 (T) then,
dualising the argument used to prove Theorem 36, we find that IT is preprojective, quasi-serial, …