Frobenius theorem (real division algebras)
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 dimensions 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)
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 dimensions 1, 2, and 4, respectively. Of these three algebras, R and C are commutative, but H is not.
has abstract
Der Satz von Frobenius, 1877 v ...... einen -Algebrenisomorphismus .
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El teorema de Frobenius, aplic ...... commutativas, pero no lo es H.
@es
Em matemática, mais especifica ...... ativa) álgebra de octônios ().
@pt
En mathématiques, plus spécifi ...... ivision : celle des octonions.
@fr
In mathematics, more specifica ...... are commutative, but H is not.
@en
Twierdzenie Frobeniusa – twier ...... Ferdinanda Georga Frobeniusa.
@pl
Теоре́ма Фробе́ниуса — одна из ...... Ф. Г. Фробениусом в 1877 году.
@ru
数学の抽象代数学において、フロベニウスの定理（ふろべにうすの ...... い実数上の結合的多元体は四元数体しかないことを証明している。
@ja
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Der Satz von Frobenius, 1877 v ...... n Multiplikation. Da und Sei .
@de
El teorema de Frobenius, aplic ...... commutativas, pero no lo es H.
@es
Em matemática, mais especifica ...... ativa) álgebra de octônios ().
@pt
En mathématiques, plus spécifi ...... commutatif ℍ des quaternions.
@fr
In mathematics, more specifica ...... are commutative, but H is not.
@en
Twierdzenie Frobeniusa – twier ...... Ferdinanda Georga Frobeniusa.
@pl
Теоре́ма Фробе́ниуса — одна из ...... Ф. Г. Фробениусом в 1877 году.
@ru
数学の抽象代数学において、フロベニウスの定理（ふろべにうすの ...... い実数上の結合的多元体は四元数体しかないことを証明している。
@ja
label
Frobenius theorem (real division algebras)
@en
Satz von Frobenius (reelle Divisionsalgebren)
@de
Teorema de Frobenius (álgebra)
@es
Teorema de Frobenius
@pt
Théorème de Frobenius (algèbre)
@fr
Twierdzenie Frobeniusa o algebrach z dzieleniem nad ciałem liczb rzeczywistych
@pl
Теорема Фробениуса
@ru
フロベニウスの定理 (代数学)
@ja