• 1 Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University

[This article has been retracted by the journal ; see Retractation notice https://doi.org/10.2478/cm-2019-0014]A QTAG-module M is an α-module, where α is a limit ordinal, if M/Hβ (M) is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 ≤ ω 1 we prove that an α-large submodule L of an ω 1-module M is summable if and only if M is summable.

• 16K20 - Finite-dimensional division rings

• 1 HAL