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

Document Type : Original Manuscript

Authors

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.

Abstract

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 $\Gamma(M(X, \mathcal{A}, \mu))$.

Keywords

References

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Journal of Algebraic Systems
Volume 9, Issue 2
January 2022
Pages 175-192

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