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math.RA2024★ 2 cited
Non-associative versions of Hilbert's basis theorem
Per Bäck, Johan Richter
We prove several new versions of Hilbert's basis theorem for non-associative Ore extensions, non-associative skew Laurent polynomial rings, non-associative skew power series rings,…
math.RA2024★ 2 cited
Flipped non-associative polynomial rings and the Cayley-Dickson construction
Masood Aryapoor, Per Bäck
We introduce and study flipped non-associative polynomial rings. In particular, we show that all Cayley-Dickson algebras naturally appear as quotients of a certain type of such rin…