STRUCTURE OF ZERO-DIVISOR GRAPHS ASSOCIATED TO RING OF INTEGER MODULO n | ||
| Journal of Algebraic Systems | ||
| دوره 11، شماره 1، آذر 2023، صفحه 1-14 اصل مقاله (163.54 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11719.1599 | ||
| نویسندگان | ||
| Shariefuddin Pirzada* ؛ Aaqib Altaf؛ Saleem Khan | ||
| Department of Mathematics, University of Kashmir, Srinagar, India. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| zero-divisor graph؛ integers modulo ring؛ Eulers's totient function | ||
| مراجع | ||
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