We show the inheritance of summable property for certain fully invariant submodules by the QTAG-modules and vice versa. Important generalizations and extensions of classical results in this direction are also established.
Rafiquddin, Ayazul Hasan and Mohammad Fareed Ahmad
A QTAG-module M is an α-module, where α is a limit ordinal, if M/Hβ (M) is totally projective for every ordinal β < α. In the present paper α-modules are studied with the help of α-pure submodules, α-basic submodules, and α-large submodules. It is found that an α-closed α-module is an α-injective. For any ordinal ω ≤ α ≤ ω1 we prove that an α-large submodule L of an ω1-module M is summable if and only if M is summable.