Document Type : Original Manuscript

Authors

Department of Mathematics, University of Kashmir, Srinagar, India.

10.22044/jas.2022.11719.1599

Abstract

For a commutative ring $R$ with identity $1\neq 0$, let $Z^{*}(R)=Z(R)\setminus \lbrace 0\rbrace$ be the set of non-zero zero-divisors of $R$, where $Z(R)$ is the set of all zero-divisors of $R$. The zero-divisor graph of $R$, denoted by $\Gamma(R)$, is a simple graph whose vertex set is $Z^{*}(R)=Z(R)\setminus \{0\}$ and two vertices of $Z^*(R)$ are adjacent if and only if their product is $0$. In this article, we find the structure of the zero-divisor graphs $\Gamma(\mathbb{Z}_{n})$, for $n=p^{N_1}q^{N_2}r$, where $2<p<q<r$ are primes and $N_1$ and $N_2$ are positive integers.

Keywords

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