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PreprintCC BY 4.0arXiv

A Bézout domain that is not an elementary divisor domain

  • Christian Hägg
  • Anders Mörtberg
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Abstract

We settle in the negative the longstanding question whether every Bézout domain is an elementary divisor domain by constructing a Bézout domain over which an explicit 2× 2 matrix has no Smith normal form. The obstruction is topological and is detected by the Möbius line bundle.

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Cite

BibTeXRIS
BibTeX
@misc{hagg2026bézout,
  title = {{A Bézout domain that is not an elementary divisor domain}},
  author = {Christian Hägg and Anders Mörtberg},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35229},
  eprint = {2609.35229},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35229},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Bézout domain that is not an elementary divisor domain
AU  - Christian Hägg
AU  - Anders Mörtberg
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35229
UR  - https://arxiv.org/abs/2609.35229
AB  - We settle in the negative the longstanding question whether every Bézout domain is an elementary divisor domain by constructing a Bézout domain over which an explicit 2× 2 matrix has no Smith normal form. The obstruction is topological and is detected by the Möbius line bundle.
ER  -