Hv-module of functions over Hv-ring of arithmetics and it's fundamental module

Abstract

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 Hv-module of complex valued functions over the Hv-ring of arithmetics, classify its complete parts, the strongly regular relations on it and identify its fundamental module. © 2024 M. Al Tahan, published by Sciendo.

Keywords Complete part, Fundamental module, Fundamental relation, Fundamental ring, Hv-module