@article{Hamidi2024, 
author = {Mohammad Hamidi and Irina Cristea},
title = {Hyperideal-based zero-divisor graph of the general hyperring              Z              n},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {15891-15910},
keywords = {general hyperring, hyperideal, absorbing elements, hyperideal-based zero-divisor graph},
url = {https://www.sciopen.com/article/10.3934/math.2024768},
doi = {10.3934/math.2024768},
abstract = {The aim of this paper is to introduce and study the concept of a hyperideal-based zero-divisor graph associated with a general hyperring. This is a generalized version of the zero-divisor graph associated with a commutative ring. For any general hyperring    R having a hyperideal    I, the    I-based zero-divisor graph        Γ          (      I      )        (  R  ) associated with    R is the simple graph whose vertices are the elements of    R  ∖  I having their hyperproduct in    I, and two distinct vertices are joined by an edge when their hyperproduct has a non-empty intersection with    I. In the first part of the paper, we concentrate on some general properties of this graph related to absorbing elements, while the second part is dedicated to the study of the    I-based zero-divisor graph associated to the general hyperring              Z        n   of the integers modulo    n, when    n  =  2      p    m    q, with    p and    q two different odd primes, and fixing the hyperideal    I.}
}