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On quasi primary ideals and weakly quasi primary ideals | ||
| Caspian Journal of Mathematical Sciences | ||
| مقاله 9، دوره 13، شماره 1 - شماره پیاپی 25، 2024، صفحه 106-117 اصل مقاله (144.81 K) | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2024.26781.1684 | ||
| نویسنده | ||
| Alireza Alehafttan* | ||
| Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran | ||
| تاریخ دریافت: 08 اسفند 1402، تاریخ بازنگری: 13 اردیبهشت 1403، تاریخ پذیرش: 01 خرداد 1403 | ||
| چکیده | ||
| Let $R$ be a commutative ring with identity. A proper ideal $Q$ of $R$ is called quasi primary (weakly quasi primary) if whenever $ab\in Q$ ($0\neq ab\in Q$) for some $a,b \in R$, then $a\in \sqrt{Q}$ or $b\in \sqrt{Q}$. In this paper, we study quasi primary (weakly quasi primary) ideals which are generalization of prime ideals. Our study provides an analogous to the prime avoidance theorem. We determined the Noetherian rings that each ideal of them is quasi primary and the rings that each ideal of them is weakly quasi primary. Besides giving various examples and characterizations of quasi primary and weakly quasi primary and we investigate the relations between them. | ||
| کلیدواژه‌ها | ||
| prime ideal؛ quasi primary ideal؛ weakly quasi primary ideal | ||
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آمار تعداد مشاهده مقاله: 423 تعداد دریافت فایل اصل مقاله: 504 |
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