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On the generalization of torsion functor and P-semiprime modules over noncommutative rings | ||
Journal of Hyperstructures | ||
دوره 13، شماره 1، 2024، صفحه 1-14 اصل مقاله (299.88 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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