ZERO-DIVISOR GRAPH OF THE RINGS OF REAL MEASURABLE FUNCTIONS WITH THE MEASURES
نویسندگان
1 Department of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran.
2 Department of Mathematical Sciences, Shahrekord University, P.O. Box 115, City, Country.
doi
10.22044/jas.2020.9745.1474چکیده
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 of$M(X, \mathcal{A}, \mu)$ and measure properties of $(X, \mathcal{A}, \mu)$.Finally, we investigate the continuity properties of $\Gamma(M(X, \mathcal{A}, \mu))$.
