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

Let M(X, \mathcal{A}, \mu) be the ring of real-valued measurable functionson a measurable space (X, \mathcal{A}) with measure \mu.In this paper, we study the zero-divisor graph of M(X, \mathcal{A}, \mu),denoted by \Gamma(M(X, \mathcal{A}, \mu)).We give the relationships among graph properties of \Gamma(M(X, \mathcal{A}, \mu)), ring properties ofM(X, \mathcal{A}, \mu) and measure properties of (X, \mathcal{A}, \mu).Finally, we investigate the continuity properties of \Gamma(M(X, \mathcal{A}, \mu)).

کلیدواژه ها:

Rings of measurable functions ، Measure space ، zero-divisor graph ، Continuous function