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α -modules and generalized submodules

Rafiquddin Rafiquddin, Ayazul Hasan, Mohammad Fareed Ahmad (2019)

Communications in Mathematics

A QTAG-module M is an α -module, where α is a limit ordinal, if M / H β ( 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.

Currently displaying 161 – 180 of 188