SOME ALGEBRAIC AND MEASURE THEORETIC PROPERTIES OF THE RINGS OF MEASURABLE FUNCTIONS
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, Shahrekord, Iran.
doi
10.22044/jas.2023.12150.1633چکیده
Let $M(X, \mathcal{A}, \mu)$ be the ring of real-valued measurable functions on a measure space $(X, \mathcal{A}, \mu)$. In this paper, we show that the maximal ideals of $M(X, \mathcal{A}, \mu)$ are associated with the special measurable sets in $\mathcal{A}$. We also study some other algebraic properties of $M(X, \mathcal{A}, \mu)$.
