Hilbert’s Basis Theorem for Noncommutative, Nonassociative Polynomial Rings

Abstract: In this talk, I will introduce Ore extensions, the principal noncommutative generalization of polynomial 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 provides 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 connection between such algorithms and the left and right Noetherianity of these rings. This talk is based on joint work with Masood Aryapoor.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar