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PreprintarXiv licencearXiv

Composition factors and finite representation type

  • Liang Chen
  • Zhenxian Chen
  • Yongyi Wen
  • Weiheng Xia
Open at sourcePDFDOICite

Abstract

We prove that an Artin algebra has finite representation type if its indecomposable finitely generated modules are determined, up to isomorphism, by their composition factors. This gives an affirmative answer to the conjecture on composition factors and finite representation type recorded by Auslander, Reiten and Smalo.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026composition,
  title = {{Composition factors and finite representation type}},
  author = {Liang Chen and Zhenxian Chen and Yongyi Wen and Weiheng Xia},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38813},
  eprint = {2610.38813},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38813},
}
RIS
TY  - UNPB
TI  - Composition factors and finite representation type
AU  - Liang Chen
AU  - Zhenxian Chen
AU  - Yongyi Wen
AU  - Weiheng Xia
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38813
UR  - https://arxiv.org/abs/2610.38813
AB  - We prove that an Artin algebra has finite representation type if its indecomposable finitely generated modules are determined, up to isomorphism, by their composition factors. This gives an affirmative answer to the conjecture on composition factors and finite representation type recorded by Auslander, Reiten and Smalo.
ER  -