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Hilbert's basis theorem for Poisson Ore extensions

  • Per Bäck
  • Patrik Lundström
  • Johan Öinert
  • Johan Richter
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Abstract

We prove an analogue of Hilbert's basis theorem for Poisson Ore extensions and Poisson Laurent Ore extensions. We also obtain corresponding results for iterated Poisson Ore extensions and iterated Poisson Laurent Ore extensions associated to commuting Poisson-pairs. Finally, we give examples of Poisson Ore extensions that are Poisson-Noetherian without being Noetherian as ordinary algebras.

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Cite

BibTeXRIS
BibTeX
@misc{back2026hilberts,
  title = {{Hilbert's basis theorem for Poisson Ore extensions}},
  author = {Per Bäck and Patrik Lundström and Johan Öinert and Johan Richter},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.14660},
  eprint = {2606.14660},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.14660},
}
RIS
TY  - UNPB
TI  - Hilbert's basis theorem for Poisson Ore extensions
AU  - Per Bäck
AU  - Patrik Lundström
AU  - Johan Öinert
AU  - Johan Richter
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2606.14660
UR  - https://arxiv.org/abs/2606.14660
AB  - We prove an analogue of Hilbert's basis theorem for Poisson Ore extensions and Poisson Laurent Ore extensions. We also obtain corresponding results for iterated Poisson Ore extensions and iterated Poisson Laurent Ore extensions associated to commuting Poisson-pairs. Finally, we give examples of Poisson Ore extensions that are Poisson-Noetherian without being Noetherian as ordinary algebras.
ER  -