Some algebraic and measure theoretic properties of the rings of measurable functions

Document Type : Original Manuscript

Authors

Department of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran.

Abstract

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

Keywords

References

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Journal of Algebraic Systems

Articles in Press, Accepted Manuscript
Available Online from 09 April 2024

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