On Reduced Submodules of Finite Dimensional Modules and a Generalization of Torsion Functor
| dc.contributor.advisor | David Ssevviiri | |
| dc.contributor.author | Teklemichael Worku | |
| dc.date.accessioned | 2025-08-17T22:31:36Z | |
| dc.date.available | 2025-08-17T22:31:36Z | |
| dc.date.issued | 2025-03-10 | |
| dc.description.abstract | Let k be a field with characteristic zero, R be the ring k[x1, ・ ・ ・ , xn] and P be a monomial ideal of R. We study the Artinian local algebra RP when considered as an R-module M. We show that the largest reduced submodule of M,R(M), coincides with both the socle of M and the k-submodule of M generated by all outside corner elements of the Young diagram associated with M. we further study properties of reduced submodules, in particular R(M). Let R be an associative Noetherian unital noncommutative ring. We introduce the functor PΓP over the category of R-modules and use it to characterize P-semiprime. We also show that the Greenless-May type Duality (GM) and Matlis Greenless-May Equality(MGM) hold over the full subcategory of R-Mod consisting of P-semiprime and P-semisecond modules. Finally, we generate a one-sided right ideal PΓP (R), which gives an equivalent formulation to solve K¨othe conjecture. | |
| dc.identifier.uri | https://etd.aau.edu.et/handle/123456789/6908 | |
| dc.language.iso | en_US | |
| dc.publisher | Addis Ababa University | |
| dc.subject | Reduced Submodules | |
| dc.subject | Finite Dimensional Modules | |
| dc.subject | Generalization | |
| dc.subject | Torsion Functor | |
| dc.title | On Reduced Submodules of Finite Dimensional Modules and a Generalization of Torsion Functor | |
| dc.type | Thesis |