solrize on Nostr: after the complex numbers you get the quaternions (take away commutativity), then the ...

after the complex numbers you get the quaternions (take away commutativity), then the octonions (take away associativity too), are there still invariants to remove one by one as you reach the 16-ions (sedenions), 32-ions, etc.? Is there some cool algebra that describes them?