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On the generalization of torsion functor and P-semiprime modules over noncommutative rings | ||
| Journal of Hyperstructures | ||
| دوره 13، شماره 1، شهریور 2024، صفحه 1-14 اصل مقاله (287.3 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2024.14375.1002 | ||
| نویسندگان | ||
| Teklemichael Worku Bihonegn* 1؛ Tilahun Abebaw1؛ Nega Arega2 | ||
| 1Department of Mathematics, Addis Ababa University | ||
| 2The Namibia University of Science and Technology, Namibia | ||
| چکیده | ||
| Let R be an associative Noetherian unital noncommutative ring R. We introduce the functor PΓP over the category of R-modules and use it to characterize P-semiprime. P-semisecond R-modules also characterized by the functor PΛP. We also show that the Greenless-May Duality (GM) and Matlis Greenless-May Equality(MGM) hold over the full subcategory of R-Mod consisting of R-semiprime and R-semisecond modules. Finally, we generate a one-sided right ideal PΓP(R), which gives an equivalent formulation to solve K{\"o}the conjecture positively or negatively. | ||
| کلیدواژه‌ها | ||
| P-semisecond؛ torsion functor؛ adic completion؛ kothe conjecture | ||
| مراجع | ||
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