Representation theory is the parts of advanced topics in abstract algebra that deal with groups. Reperesentation theory in general facilitate the problems on abstract algebra by transforming into linear algebra form. There are some cases of representation theory which can be expressed as modules over ring. Let G be a group and V be a vector space over field, F . The representation of group G is a homomorphism y: G→GL(V), where GL→V is invertible automorphism from V to itself.. In this study, the representation of group was generalized by exchanging the vector spaces with modules. Furthermore, the aim of this study is not only to generalize the representation of group over vector space but also to investigate conditions that formed on representation of group over modules. Results regarding the properties of representation of group over modules have been obtained in this study.
