Wedderburn-Artin theorem

If R is a left semisimple ringMathworldPlanetmathPlanetmath, then


where each Di is a division ring and 𝕄ni(Di) is the matrix ring over Di, i=1,2,,r. The positive integer r is unique, and so are the division rings (up to permutationMathworldPlanetmath).

Some immediate consequences of this theorem:

This theorem is a special case of the more general theorem on semiprimitive rings.

Title Wedderburn-Artin theorem
Canonical name WedderburnArtinTheorem
Date of creation 2013-03-22 14:19:08
Last modified on 2013-03-22 14:19:08
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 14
Author CWoo (3771)
Entry type Theorem
Classification msc 16D70
Synonym structure theorem on semisimple rings
Synonym Artin-Wedderburn theorem
Related topic SemiprimitiveRing