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:

    This is the gospel of labour, ring it, ye bells of the kirk!
    The Lord of Love came down from above, to live with the men who work.
    This is the rose that He planted, here in the thorn-curst soil:
    Heaven is blest with perfect rest, but the blessing of Earth is toil.
    Henry Van Dyke (1852–1933)