Theoretical analysis establishes an analogue of Hilbert's basis theorem in Poisson Ore extensions, demonstrating that Poisson–Noetherian structures can exist outside standard Noetherian rings.
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.
No takes yet. Share an insight, caveat, or question.
Bäck et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: