ZERO-DIVISOR GRAPH OF THE RINGS OF REAL MEASURABLE FUNCTIONS WITH THE MEASURES | ||
| Journal of Algebraic Systems | ||
| دوره 9، شماره 2، فروردین 2022، صفحه 175-192 اصل مقاله (299.24 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2020.9745.1474 | ||
| نویسندگان | ||
| H. Hejazipour1؛ A. R. Naghipour* 2 | ||
| 1Department of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran. | ||
| 2Department of Mathematical Sciences, Shahrekord University, P.O. Box 115, City, Country. | ||
| چکیده | ||
| Let $M(X, \mathcal{A}, \mu)$ be the ring of real-valued measurable functions on 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 $\Gamma(M(X, \mathcal{A}, \mu))$. | ||
| کلیدواژهها | ||
| Rings of measurable functions؛ Measure space؛ Zero-divisor graph؛ Continuous function | ||
| مراجع | ||
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