Strongly regular relations of arithmetic functions

A simple, but very useful concept in number theory is that of an arithmetic function. On the other hand, hyperstructure theory, first introduced by Marty, is a generalization of group theory and it is connected to different fields of mathematics. In our paper, we present a link between the theories of algebraic structures, hyperstructures and arithmetic functions. More precisely, we present hyperstructures of arithmetic functions and determine their fundamental groups and fundamental rings. Moreover, we study their complete parts and strongly regular relations.