studying some semisimple modules via hypergraphs

Recent studies have shown that hypergraphs are useful in solving real-life problems. hypergraphs have been successfully applied in various fields. inspiring by the importance, we shall introduce a new hypergraph assigned to a given module. by the way, vertices of this hypergraph (which we call sum hypergraph) are all nontrivial submodules of a module p and a subset e of the vertices is a hyperedge in case the sum of each two elements of e is equal to p and e is maximal with respect to this condition. some general properties of such hypergraphs are discussed. semisimple modules with length 2 are characterized by their corresponding sum hypergraphs. it is shown that the sum hypergraph assigned to a finite module p is connected if and only if p is semisimple.