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Krull-Remak-Schmidt decompositions in Hom-finite additive categories
Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review
DOI
- https://doi.org/10.1016/j.exmath.2022.12.003
Forlagets udgivne version
An additive category in which each object has a Krull-Remak-Schmidt decomposition—that is, a finite direct sum decomposition consisting of objects with local endomorphism rings—is known as a Krull-Schmidt category. A Hom-finite category is an additive category A for which there is a commutative unital ring k, such that each Hom-set in A is a finite length k-module. The aim of this note is to provide a proof that a Hom-finite category is Krull-Schmidt, if and only if it has split idempotents, if and only if each indecomposable object has a local endomorphism ring.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Expositiones Mathematicae |
| Vol/bind | 41 |
| Nummer | 1 |
| Sider (fra-til) | 220-237 |
| Antal sider | 18 |
| ISSN | 0723-0869 |
| DOI | |
| Status | Udgivet - mar. 2023 |
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