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arXiv · 2606.14660

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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Per Bäck, Patrik Lundström, Johan Öinert, Johan Richter. 2026-06-12. Hilbert's basis theorem for Poisson Ore extensions. https://doi.org/10.1002/mana.70248

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