You can't get the associative property in higher dimensions. There is something called octonions (which is not associative but has some similar tho weaker prop

You can't get the associative property in higher dimensions. There is something called octonions (which is not associative but has some similar tho weaker properties) https://en.wikipedia.org/wiki/Octonion https://en.wikipedia.org/wiki/Octonion There is a sequence of such structures, but after the Octonions you get non-zero numbers that multiply to zero: https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_constru...