H_v-module of functions over H_v-ring of arithmetics and it’s fundamental module

After introducing the definition of hypergroups by Marty, the study of hyperstructures and its connections with other fields has been of great importance. In this paper, we continue the investigation between hyperstructure theory and number theory. More precisely, we define an H_v-module of complex valued functions over the H_v-ring of arithmetics, classify its complete parts, the strongly regular relations on it and identify its fundamental module.