A Module Theory Approach on Generalization of Maschke Theorem and Schur’s Lemma in Representation Theory

Abstract

In this work we study representations of finite abelian groups over module over a principal ideal domain. Let G be a finite abelian group and M a module over a principal ideal domain R. A representation of G over M is a group homomorphism from G to the automorphisms on M over R. We use the fact that this M can be represented as an R[G]-module to generalize Maschke Theorem and Schur’s Lemma.