The embedding of the components of the auslander-reiten quiver of an artin algebra containing no oriented cycle1
作者:
Size Li,
期刊:
Communications in Algebra
(Taylor Available online 2000)
卷期:
Volume 28,
issue 10
页码: 4635-4645
ISSN:0092-7872
年代: 2000
DOI:10.1080/00927870008827109
出版商: Gordon and Breach Science Publishers Ltd.
数据来源: Taylor
摘要:
LetAbe an artin algebra. Let Γ be a component of the Auslander-Reiten Quiver ΓAand Γ contain no oriented cycle. If Γ is stable or semi-stable, then the structure of Γ is known. Here, we are going to consider general component which may contain both injective vertices and projective vertices at the same time. We will show that Γ can be embedded in some Δ with Δ isomorphic to a section of Γ if and only if every possible path from an injective vertex to a projective vertex is sectional. This result generalizes part of Zhang’s theorem and the corresponding part of Liu’s theorem.
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