On the existence of hyperrings associated to arithmetic functions
type: Item
instance of: scholarly article
title: On the existence of hyperrings associated to arithmetic functions
zbMATH Open document ID: 1383.16047
author: Yong-Cai Geng
author: Sumit K. Garg
published in: Journal of Number Theory
publication date: 2017-01-23T00:00:00Z
review text: 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.
reviewed by: Stefan Veldsman
Mathematics Subject Classification ID: 16Y99
Mathematics Subject Classification ID: 20N20
Mathematics Subject Classification ID: 11A25
zbMATH DE Number: 6676810
zbMATH Keywords: arithmetic functions
zbMATH Keywords: hyperstructure
zbMATH Keywords: hyperring
MaRDI profile type: Publication
full work available at URL: j.jnt.2016.10.017
OpenAlex ID: W2559728490
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DOI: 10.1016/J.JNT.2016.10.017
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description: scientific article; zbMATH DE number 6676810