Etudiant : JAARI AZIZ

Filière : Master Mathématiques Pures (MMP)

Encadrant : Pr. EL KHALFAOUI RACHIDA

Annèe : 2022

Résumé : 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 if and only if xy = 0. Recently, it has been shown that for any finite ring R, Γ(R) has an even number of edges. Here we give a simple proof for this result. In this paper we investigate some properties of zero−divisor graphs of matrix rings and group rings. Among other results, we prove that for any two finite commutative rings R, S with identity and n, m ≥ 2„ if Γ(Mn(R)) ≃ Γ(Mm(S)), then n = m, |R| = |S|, and Γ(R) ≃ Γ(S).