ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS | ||
| Journal of Algebraic Systems | ||
| مقاله 12، دوره 7، شماره 2، فروردین 2020، صفحه 257-269 اصل مقاله (180.38 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2019.8150.1399 | ||
| نویسنده | ||
| M. Abedi* | ||
| Esfarayen University of Technology, Esfarayen, North Khorasan, Iran. | ||
| چکیده | ||
| We study primary ideals of the ring $\mathcal{R}L$ of real-valued continuous functions on a completely regular frame $L$. We observe that prime ideals and primary ideals coincide in a $P$-frame. It is shown that every primary ideal in $\mathcal{R}L$ is contained in a unique maximal ideal, and an ideal $Q$ in $\mathcal{R}L$ is primary if and only if $Q \cap\mathcal{R}^*L$ is a primary ideal in $\mathcal{R}^*L$. We show that every pseudo-prime (primary) ideal in $\mathcal{R}L$ is either an essential ideal or a maximal ideal which is at the same time a minimal prime ideal. Finally, we prove that if $L$ is a connected frame, then the zero ideal in $\mathcal{R}L$ is decomposable if and only if $L={\bf2}$. | ||
| کلیدواژهها | ||
| Frame؛ primary ideal؛ pseudo-prime ideal؛ ring of continuous real-valued functions؛ decomposable ideal | ||
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آمار تعداد مشاهده مقاله: 549 تعداد دریافت فایل اصل مقاله: 646 |
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