Division Ring - Ring Theorems

Ring Theorems

Wedderburn's little theorem: All finite division rings are commutative and therefore finite fields. (Ernst Witt gave a simple proof.)

Frobenius theorem: The only finite-dimensional division algebras over the reals are the reals themselves, the complex numbers, and the quaternions.

Read more about this topic:  Division Ring

Famous quotes containing the word ring:

    “Genius resembles a bell; in order to ring it must be suspended into pure air, and when a foreign body touches it, its joyful tone is silenced.”
    —Franz Grillparzer (1791–1872)