[lanstin]

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 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_constru...