Different characterizations of large submodules of QTAG-modules (Q2421738)

Summary: A module \(M\) over an associative ring \(R\) with unity is a \textit{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 \(\Sigma\)-modules, summable modules, \(\sigma\)-summable modules, and so on.