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Abstract 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… Click to show full abstract
Abstract 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 , + , ⋅ ) .
Journal Title: Journal of Number Theory
Year Published: 2017
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