The sedenions are a 16 dimensional nonassociative algebra over the reals.

The sedenions are the 16 dimensional nonassociative normed algebra obtained by applying the Caley-Dickson-Construction to the octonions.

Every sedenion has a multiplicative inverse, but due to the nonassociative nature of the algebra, the algebra also has zero divisors. For this reason, sources disagree on calling it a "division algebra."