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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
DOI: https://doi.org/10.1090/S0002-9939-1982-0660596-0
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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Article copyright: © Copyright 1982 American Mathematical Society