Hilbert's basis theorem for Poisson Ore extensions
arXiv:2606.14660
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.
8 pages; added Remark 2 and Lemma 3 on localization, simplifying the Laurent case of Proposition 5 and the Laurent cases of Theorems 1 and 6, with some additional minor corrections and clarifications