Reducible Property of a Finitely Generated Module

In the article, G-invariant element, , and other concepts were introduced, Several lemmas were proved to use these concepts, Finally, it had been proved that let F be a field whose characteristic dose not divide |G|. Then every finitely generated F[G] module is completely reducible.Key words: finitely generated R[G] module; B-projective; R-homomorphism; R-homomorphism