Composition Algebras
Normed division algebras are a special case of composition algebras. Composition algebras are unital algebras with a multiplicative quadratic form. General composition algebras need not be division algebras, however—they may contain zero divisors. Over the real numbers this gives rise to three additional algebras: the split-complex numbers, the split-quaternions, and the split-octonions.
Read more about this topic: Normed Division Algebra
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“The proposed Constitution ... is, in strictness, neither a national nor a federal constitution; but a composition of both.”
—James Madison (1751–1836)
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