Gabriel-Roiter inclusions and Auslander-Reiten theory

JOURNAL OF ALGEBRA

卷:324

Article

Ringel, Claus Michael

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

DOI  :  10.1016/j.jalgebra.2010.09.003

来源: Elsevier

【 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

【 授权许可】

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