Frobenius theorem (real division algebras)
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In mathematics, more specifically in abstract algebra, the Frobenius theorem, proved by Ferdinand Georg Frobenius in 1877, characterizes the finite dimensional associative division algebras over the real numbers. The theorem proves that the only associative division algebra which is not commutative over the real numbers are the quaternions.
If D is a finite dimensional division algebra over the real numbers R then one of the following cases holds
- D = R
- D = C ( complex numbers)
- D isomorphic to H (quaternions)
Reference
- Yuri Bahturin (1993) Basic Structures of Modern Algebra, Kluwer Acad. Pub. pp.30-2 [ISBN 0792324595].
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