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

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