Different Characterizations of Large Submodules of QTAG-Modules

A module over an associative ring with unity is a -module if every finitely generated submodule of any homomorphic image of 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 of is large in if , for every basic submodule of 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 -modules, summable modules, -summable modules, and so on.

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