Gabriel-Roiter inclusions and Auslander-Reiten theory

[摘要] Let A 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 submodule of Y then Y is shown to be a factor module of an indecomposable module M such that there exists an irreducible monomorphism X -> M We also will prove that the monomorphisms in a homogeneous tube are Gabriel-Roiter inclusions provided the tube contains a module whose endomorphism ring is a division ring (C) 2010 Elsevier Inc All rights reserved

[发布日期] 2010-12-15

[关键词] Artin algebras;Indecomposable modules;Auslander-Reiten theory;Gabriel-Roiter inclusions