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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on preprojective partitions over hereditary Artin algebras


Author: Gordana Todorov
Journal: Proc. Amer. Math. Soc. 85 (1982), 523-528
MSC: Primary 16A35
MathSciNet review: 660596
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Abstract: If $ \Lambda $ is an artin algebra there is a partition of $ \operatorname{ind} \Lambda $, the category of indecomposable finitely generated $ \Lambda $-modules, $ \operatorname{ind} \Lambda = { \cup _{i \geqslant 0}}{\underline{\underline{P}}_i}$, called the preprojective partition. We show that $ \underline{\underline{P}}_i$ can be easily constructed for hereditary artin algebras, if $ \underline{\underline{P}}_{i - 1}$ is known: $ A$ is in $ \underline{\underline{P}}_i$ if and only if $ A$ is not in $ \underline{\underline{P}}_{i - 1}$ and there is an irreducible map $ B \to A$, where $ B$ is in $ \underline{\underline{P}}_{i - 1}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660596-0
PII: S 0002-9939(1982)0660596-0
Article copyright: © Copyright 1982 American Mathematical Society