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SUMMARY:Per Bäck (Mälardalen University\, Sweden)
DTSTART:20260504T150000Z
DTEND:20260504T160000Z
DTSTAMP:20260513T133623Z
UID:ENAAS/172
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/172/">
 Hilbert’s Basis Theorem for Noncommutative\, Nonassociative Polynomial R
 ings</a>\nby Per Bäck (Mälardalen University\, Sweden) as part of Europe
 an Non-Associative Algebra Seminar\n\n\nAbstract\nIn this talk\, I will in
 troduce Ore extensions\, the principal noncommutative generalization of po
 lynomial rings\, and recall how Hilbert’s Basis Theorem extends to them.
  I will then present generalized nonassociative Ore extensions (GNOEs)\, a
  natural extension of Ore extensions to the nonassociative setting that pr
 ovides a unifying framework for nonassociative\, noncommutative polynomial
  rings\, including examples such as the Cayley–Dickson algebras. Finally
 \, I will show that Hilbert’s Basis Theorem generalizes to GNOEs via the
  existence of Euclidean division algorithms\, revealing a new and direct c
 onnection between 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/
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