On generalized standard Auslander-Reiten components having only finitely many non-directing modules

JOURNAL OF ALGEBRA

卷:279

Article

Smith, D

关键词: quasi-directed components;    generalized standard components;    directed components;    Auslander-Reiten quiver;    Laura algebras;    weakly shod algebras;   

DOI  :  10.1016/j.jalgebra.2004.03.022

来源: Elsevier

【 摘 要 】

Let Gamma be a connected component of the Auslander-Reiten quiver Gamma (mod A) of an Artin algebra. We show that Gamma is quasi-directed if and only if the paths in ind A, having end-points in Gamma, satisfy certain conditions. Moreover, we describe the shapes of such components and identify the classes of algebras to which they are related. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

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