On the existence of hyperrings associated to arithmetic functions
The authors study hyperoperations on the set \(G\) of arithmetic functions. A hyperoperation on \(G\) is a function that assigns to an ordered pair of elements from \(G\) a uniquely defined subset of \(G.\) In particular, two such operations \(\ast \) and \(\circ \) on \(G\) are given and their elementary algebraic properties are determined. Later these operations are called \(+\) and \(\cdot \) respectively. One of the main results is to show that the set of all constant arithmetic functions is a so called Krasner hyperring with respect to these operations. The significance of this result is not clear; it seems that these operations on constant functions reduce to the usual addition and multiplication of complex numbers and \(M\) (the set of all constant arithmetic functions on \(G\)) is actually just the complex field. The paper should be read with care. It contains a number of misprints and/or confusing notations.
scientific article; zbMATH DE number 6676810
scientific article