Different Characterizations of Large Submodules of QTAG-Modules. (3rd January 2017) - Sikander, Fahad; Mehdi, Alveera; Naji, Sabah A. R. K.
Abstract : A module M over an associative ring R with unity is a Q T A G -module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. The study of large submodules and its fascinating properties makes the theory of QTAG-modules more interesting. A fully invariant submodule L of M is large in M if L + B = M, for every basic submodule B of M . The impetus of these efforts lies in the fact that the rings are almost restriction-free. This motivates us to find the necessary and sufficient conditions for a submodule of a QTAG-module to be large and characterize them. Also, we investigate some properties of large submodules shared by Σ -modules, summable modules, σ -summable modules, and so on.