I was looking into hyper complex numbers https://en.wikipedia.org/wiki/Hypercomplex_number where it stated that under Cayley–Dickson construction for "$\{1,i_1,...i_{2^n-1}\}$... in $16$ or more dimensions $(n ≥ 4)$ these algebras also have zero-divisors."
My questions were:
1) which branch of mathematics did hypercomplex number belong to?
2' Could you gave me a prove that at and beyond $e_{16}$ had zero divisor?
This is the area of Composition Algebras. On page 67 in "On Quaternions and Octonions" by Smith and Conway they prove Hurwitz's theorem that the norm of a product equals the product of the norms only in dimensions 1, 2, 4, and 8 (real, complex, quaternion, and octonion numbers). This then leads to that e16 and beyond has a zero divisor. Geometric algebra is another related area.