Brahim El Alaoui

collaborators

3 papers

math.AC2024

The extended zero-divisor graph of the amalgamated duplication of a ring along an ideal

Brahim El Alaoui, Raja L'hamri

Let $R$ be a commutative ring and $I$ be an ideal of $R$ . The amalgamated duplication of $R$ along $I$ is the subring $R ⋈ I := {(r, r + i) ∣ r \in R, i \in I}$ of $R \times R$ . This p…

math.AC2023

Partitioning zero-divisor graphs of finite commutative rings into global defensive alliances

Driss Bennis, Brahim El Alaoui

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 vertice…

math.AC2023

Rings whose associated extended zero-divisor graphs are complemented

Driss Bennis, Brahim El Alaoui, Raja L'hamri

Let $R$ be a commutative ring with identity $1 \neq = 0$ . In this paper, we continue the study started in [10] concerning when the extended zero-divisor graph of $R$ , $Γ (R)$ ,…