Sedenion

In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the reals; they are obtained by applying the Cayley–Dickson construction to the octonions, and as such the octonions are a subalgebra of the sedenions. Unlike the octonions, the sedenions are not an alternative algebra. Applying the Cayley–Dickson construction to the sedenions yields a 32-dimensional algebra, sometimes called the 32-ions or Trigintaduonions. It is possible to apply the Cayley–Dickson construction to the sedenions infinitely many times.


In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the reals; they are obtained by applying the Cayley–Dickson construction to the octonions, and as such the octonions are a subalgebra of the sedenions. Unlike the octonions, the sedenions are not an alternative algebra. Applying the Cayley–Dickson construction to the sedenions yields a 32-dimensional algebra, sometimes called the 32-ions or Trigintaduonions. It is possible to apply the Cayley–Dickson construction to the sedenions infinitely many times.
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