Different Characterizations of Large Submodules of QTAG-Modules

Abstract EN

A module M over an associative ring R with unity is a QTAG-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.