@article {
author = {Hejazipour, H. and Naghipour, A.},
title = {ZERO-DIVISOR GRAPH OF THE RINGS OF REAL MEASURABLE FUNCTIONS WITH THE MEASURES},
journal = {Journal of Algebraic Systems},
volume = {9},
number = {2},
pages = {175-192},
year = {2022},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2020.9745.1474},
abstract = {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 $\Gamma(M(X, \mathcal{A}, \mu))$.},
keywords = {Rings of measurable functions,Measure space,zero-divisor graph,Continuous function},
url = {https://jas.shahroodut.ac.ir/article_2191.html},
eprint = {https://jas.shahroodut.ac.ir/article_2191_21a43a34fff3e583e0985cad32831aa1.pdf}
}