hamidreza dorbidi

Let R be a noncommutative ring with unity and Z(R) be its centre. The commuting graph of R denoted by (R) is a graph whose vertices are noncentral elements of R and two distinct vertices x and y are adjacent if and only if xy = yx. Let F be a finite field. In this paper, we show that if (R) ∼= (M3(F)) and Z(R) is a field, then R ∼= M3(F). In particular, if (R) ∼= (M3(Fp)), then R ∼= M3(Fp).