BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Per Bäck (Mälardalen University\, Sweden) DTSTART:20260504T150000Z DTEND:20260504T160000Z DTSTAMP:20260423T035626Z UID:ENAAS/172 DESCRIPTION:Title: Hilbert’s Basis Theorem for Noncommutative\, Nonassociative Polynomial R ings\nby Per Bäck (Mälardalen University\, Sweden) as part of Europe an Non-Associative Algebra Seminar\n\nInteractive livestream: https://us02 web.zoom.us/j/7803181064\n\nAbstract\nIn this talk\, I will introduce Ore extensions\, the principal noncommutative generalization of polynomial rin gs\, and recall how Hilbert’s Basis Theorem extends to them. I will then present generalized nonassociative Ore extensions (GNOEs)\, a natural ext ension of Ore extensions to the nonassociative setting that provides a uni fying framework for nonassociative\, noncommutative polynomial rings\, inc luding examples such as the Cayley–Dickson algebras. Finally\, I will sh ow that Hilbert’s Basis Theorem generalizes to GNOEs via the existence o f Euclidean division algorithms\, revealing a new and direct connection be tween such algorithms and the left and right Noetherianity of these rings. This talk is based on joint work with Masood Aryapoor.\n LOCATION:https://researchseminars.org/talk/ENAAS/172/ URL:https://us02web.zoom.us/j/7803181064 END:VEVENT END:VCALENDAR