Group ring of finite group over field of characteristic not dividing its order is semisimple Artinian

From Groupprops
Jump to: navigation, search

Statement

Suppose G is a finite group and K is a field whose characteristic does not divide the order of G. Then, the group ring K[G] (i.e., the group ring of G over K is a semisimple Artinian ring. In particular, it is a finite-dimensional semisimple algebra over K.

Related facts