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PreprintCC BY-SA 4.0arXiv

A Counterexample to the Open Question on Object Ideals

  • Qikai Wang
  • Yuxiao Wang
  • Haiyan Zhu
Open at sourcePDFDOICite

Abstract

We give a counterexample to completeness descent from ideal cotorsion pairs to their objects. A radical-square-zero algebra on the two-cycle gives a finite-dimensional example. The construction is intrinsically non-weakly-idempotent-complete.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026counterexample,
  title = {{A Counterexample to the Open Question on Object Ideals}},
  author = {Qikai Wang and Yuxiao Wang and Haiyan Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14382},
  eprint = {2609.14382},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14382},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - A Counterexample to the Open Question on Object Ideals
AU  - Qikai Wang
AU  - Yuxiao Wang
AU  - Haiyan Zhu
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14382
UR  - https://arxiv.org/abs/2609.14382
AB  - We give a counterexample to completeness descent from ideal cotorsion pairs to their objects. A radical-square-zero algebra on the two-cycle gives a finite-dimensional example. The construction is intrinsically non-weakly-idempotent-complete.
ER  -