Browsing by Author "Teklemichael Worku"

Now showing 1 - 1 of 1
  • No Thumbnail Available
    Item
    On Reduced Submodules of Finite Dimensional Modules and a Generalization of Torsion Functor
    (Addis Ababa University, 2025-03-10) Teklemichael Worku; David Ssevviiri
    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.