2019
DOI: 10.2478/cm-2019-0002
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α-modules and generalized submodules

Abstract: 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 ≤ ω1 we prove that an α-large submodule L of an ω1-module M is summable if and only if M is summable. 2010 MSC: 16K20 R E T R A C T E D α-modules and generalized submodules 15 N = ∞ k=0 (N + H… Show more

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