Is there an analogy with the way the sequence from reals to complex numbers to quaternions to octonions (iterations of the Cayley-Dickson construction) loses al

Is there an analogy with the way the sequence from reals to complex numbers to quaternions to octonions (iterations of the Cayley-Dickson construction) loses algebraic properties? https://en.m.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction https://en.m.wikipedia.org/wiki/Cayley%E2%80%93Dickson_const...