Semisimple Module - Endomorphism Rings

Endomorphism Rings

• A semisimple module M over a ring R can also be thought of as a ring homomorphism from R into the ring of abelian group endomorphisms of M. The image of this homomorphism is a semiprimitive ring, and every semiprimitive ring is isomorphic to such an image.
• The endomorphism ring of a semisimple module is not only semiprimitive, but also von Neumann regular, (Lam 2001, p. 62).