SOME ALGEBRAIC AND MEASURE THEORETIC PROPERTIES OF THE RINGS OF MEASURABLE FUNCTIONS | ||
| Journal of Algebraic Systems | ||
| دوره 13، شماره 1، تیر 2025، صفحه 77-87 اصل مقاله (135.07 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2023.12150.1633 | ||
| نویسندگان | ||
| Homayon Hejazipour؛ Ali Reza Naghipour* | ||
| Department of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran. | ||
| چکیده | ||
| 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 $M(X, \mathcal{A}, \mu)$. | ||
| کلیدواژهها | ||
| Measure spaces؛ Rings of measurable functions؛ Maximal ideals؛ Prime ideals؛ Variety of ideals | ||
| مراجع | ||
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آمار تعداد مشاهده مقاله: 119 تعداد دریافت فایل اصل مقاله: 118 |
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