On the existence of hyperrings associated to arithmetic functions

JOURNAL OF NUMBER THEORY

卷:174

Article

Al Tahan, M.¹  Davvaz, B.² 

[1] Lebanese Int Univ, Dept Math, Beirut, Lebanon

[2] Yazd Univ, Dept Math, Yazd, Iran

关键词: Arithmetic functions;    Hyperstructure;    Hyperring;   

DOI  :  10.1016/j.jnt.2016.10.017

来源: Elsevier

【 摘 要 】

After introducing the definition of hyperring by Krasner, the study of hyperrings has been of great importance. In this paper, we define a new hyperoperation associated to the set G of all arithmetic functions and give a complete analysis of its properties. Also, we combine our hyperoperation (+) with an already defined hyperoperation (.) and define (G,+,.) in which we study its properties and the possibility of containing hyperring. First, we prove that (G,+,.) is a weak hyperring. Then we find the largest hyperring contained in (G,+,.). (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free