Sedenions

The Sedenions form a 16-dimensional algebra over the reals obtained by applying the [Cayley-Dickson construction]? to the octonions.

Like octonions, multiplication? of sedenions is neither commutative nor associative. Unlike octonions, it does not even have the property of being "alternative". Multiplication is alternative if:

P(PQ) =(PP)Q

It does however have the property of being "power associative", since:

P^aP^b = P^a+b

for natural numbers a and b.

The sedenions have multiplicative inverses, but they are not a division algebra. This is because they have "zero divisors", i.e. there exist non-zero sedenions P, Q such that:

PQ = QP = 0

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