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. According to the theorem, every such algebra is isomorphic to one of the following:
These algebras have real dimension 1, 2, and 4, respectively. Of these three algebras, R and C are commutative, but H is not.