Every Cayley-Dickson algebra can be viewed as a $(+,-,*,0,1)$ algebra. The reals and the complexes share the same equational identities. The quaternions have a subset of the equational identities, because they lose commutativity of multiplication. The octonions lose associativity, and the sedenions lose even more. Is the sedenions truly the last stop. Do all further Cayley-Dickson algebras have the same equational identities in that signature as the sedenions. This question is different from the tagged question, because I didn't see an answer for whether there are any equational identities that the sedenions have that any higher Cayley-Dickson algebras don't. I know that the sedenions are a power associative algebra.
2026-03-30 12:01:49.1774872109
Do you lose any more equational identities when you go past sedenions?
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