Let P be an R-module. We define a hypergraph on P where the vertices are all nontrivial submodules of P and a set Wi (such that | Wi |≥ 2) of nontrivial submodules of P forms a hyperedge provided the sum of each two distinct elements of Wi is equal to P and Wi is maximal with respect to this property. We denote such hypergraph via SUMR(P). Some general properties of such hypergraphs are considered.
