Sedenion

The sedenions form a sixteen dimensional algebra over the real numbers, obtained from the octonions by applying the Cayley-Dickson construction, the same doubling procedure that produces the complex numbers from the real numbers, the quaternions from the complex numbers, and the octonions from the quaternions. Each successive algebra produced by the Cayley-Dickson construction loses an algebraic property that the previous one had: the complex numbers lose the ordering of the real numbers, the quaternions lose commutativity, the octonions lose associativity, and the sedenions lose the property of being a division algebra, meaning that, unlike the octonions, sedenions can be nonzero and yet multiply together to give zero. Because of this loss of structure the sedenions are far less studied than the octonions, but they remain of interest to mathematicians studying hypercomplex number systems and the Cayley-Dickson construction itself.