ZERO-DIVISOR GRAPH OF THE RINGS OF REAL MEASURABLE FUNCTIONS WITH THE MEASURES

Let M(X,A,μ) be the ring of real-valued measurable functions on a measurable space (X,A) with measure μ.In this paper, we study the zero-divisor graph of M(X,A,μ),denoted by Γ(M(X,A,μ)).We give the elationships among graph properties of Γ(M(X,A,μ)), ring properties of M(X,A,μ) and measure properties of (X,A,μ).Finally, we investigate the continuity properties of Γ(M(X,A,μ))