Auslander-Reiten Components determined by their Composition Factors
Alicja Jaworska, Piotr Malicki, Andrzej Skowro\'nski
TL;DR
This paper establishes conditions under which components of the Auslander-Reiten quiver of an artin algebra can be uniquely identified by the composition factors of their indecomposable modules.
Contribution
It introduces new criteria that allow the determination of Auslander-Reiten components solely based on composition factors.
Findings
Provided sufficient conditions for component determination
Connected composition factors to Auslander-Reiten quiver structure
Enhanced understanding of module classification in artin algebras
Abstract
We provide sufficient conditions for a component of the Auslander-Reiten quiver of an artin algebra to be determined by the composition factors of its indecomposable modules.
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