<ul><li>Octonions are formed through the multiplication of 8-tuples, diverging from the properties of commutativity and associativity.</li><li>The subalgebra generated by any two elements of octonions proves to be associative, resembling the real, complex, or quaternion numbers.</li><li>Quaternions and octonions retain properties like a multiplicative inverse and norm coherence, displaying unique algebraic properties.</li><li>Sedenions, resulting from the multiplication of 16-tuples of real numbers, exhibit further loss of structure with non-commutativity, non-associativity, and possible zero products.</li></ul>

Octonions sometimes associate

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