symmetric monoidal (∞,1)-category of spectra
The sedenions are the non-associative algebra $\mathbb{S}$ over the real numbers obtained by applying the Cayley–Dickson construction to the octonions.
Although every sedenion has a multiplicative inverse, $\mathbb{S}$ is not a division algebra (which is possible since it is not associative).
Wikipedia, Sedenion