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math.RA2026
Involutions in the Cayley-Dickson construction
Masood Aryapoor, Per Bäck, Per Bäck +1
We determine all involutions in the Cayley-Dickson construction that extend the involution of the original -algebra. We also find all algebra isomorphisms between the resulting…
math.RA2024
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…
math.RA2024
Simplicity of non-associative skew Laurent polynomial rings
Per Bäck, Johan Richter
We introduce non-associative skew Laurent polynomial rings and characterize when they are simple. Thereby, we generalize results by Jordan, Voskoglou, and Nystedt and Ãinert.