… and we may choose as the module Z the immediate successor of X in the preprojective
component … Then we obtain all modules in K by calculating the relative Auslander-Reiten …

… Auslander-Reiten quiver T(A) in the following way: T(A) has as vertices representatives from
the isomorphism classes of indecomposable modules. … (A) is called preprojective provided C …

… the structure of the Auslander endash Reiten components of finite hyphen dimensional
modules for … Moreover comma this is the only preprojective component for Capital Sigma period …

… dimensional algebra with a faithful indecomposable module and with Auslander-Reiten quiver
without oriented cycle is … direct summand if and only if all preprojective modules belong to …

… Reiten have shown the existence of Auslander–Reiten sequences: for any indecomposable
non-injective module … Let P1, P2,... be the sequence of preprojective modules, with non-zero …

… module, and conversely, if E is an elementary stone, then for> 0 there exists a preprojective
module T such that T7-¹E is a tilting module… (−, A) the Auslander-Reiten translation of A. For a …

… all / ^ N, r being the Auslander-Reiten translate. We use this … 2 to treat tilting modules AT
without a preprojective, or without … Thus for a 5-module I we can consider the Auslander-Reiten …

… Our main purpose in this paper is to study the Auslander–Reiten … with modules category over
some Artin algebras. The … ) ) and the module category mod ⁢ - ⁢ Π n - 1 of the preprojective …

… module T without nonzero preprojective (equivalently, preinjective) direct summands, and
ψ is a positive automorphism of ̂B. Further, we know from [21, Corollary 3.3] and [18] that C is …

… a higher-dimensional version of Auslander’s theorem on … modules on preprojective
algebras is closely related to our study. In 6.3, we see that the work of Buan–Marsh–Reineke–Reiten–…