In this article, we give several generalizations of the concept of zero-divisor elements in a
commutative ring with identity to modules. Then, for each 𝑅-module 𝑀, we associate three …

Let R be a commutative ring with identity and M an R-module. In this paper, we associate a
graph to M, say Γ (M), such that when M= R, Γ (M) is exactly the classic zero-divisor graph …

For a commutative ring R with identity, the zero-divisor graph of R, denoted Γ (R), is the
graph whose vertices are the non-zero zero-divisors of R with two distinct vertices joined by …

In this paper, we introduce a new graph whose vertices are the non-zero zero-divisors of a
commutative ring R, and for distincts elements x and y in the set Z (R)* of the non-zero zero …

The zero-divisor graph of a ring R is defined as the directed graph Γ (R) that its vertices are
all non-zero zero-divisors of R in which for any two distinct vertices x and y, x→ y is an edge …

Let R be a commutative ring with 1, and let Z (R) denote the set of zero-divisors of R. We
define an undirected graph Γ (R) with vertices Z (R)*= Z (R)−{0}, where distinct vertices x and …

Full article: Zero-Divisor Graphs of Matrices Over Commutative Rings Skip to Main Content
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An element a in a ring R is called a strong zero-divisor if, either (a)(b)= 0 or (b)(a)= 0, for
some 0\= b∈ R ((x) is the ideal generated by x∈ R). Let S (R) denote the set of all strong …

Zero-divisor graphs of finite commutative rings: a survey Page 1 Surveys in Mathematics and
its Applications ISSN 1842-6298 (electronic), 1843-7265 (print) Volume 15 (2020), 371 – 397 …

Let R be a commutative ring. In this paper, we study the annihilatorideal-based zero-divisor
graph by replacing the ideal I of R with the idealAnnR (M) for an R-module M. Also, we …