α-modules and generalized submodules

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Abstract

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 ωαω1 we prove that an α-large submodule L of an ω1-module M is summable if and only if M is summable.

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CiteScore 2018: 0.4

SCImago Journal Rank (SJR) 2018: 0.193
Source Normalized Impact per Paper (SNIP) 2018: 0.696

Mathematical Citation Quotient (MCQ) 2018: 0.17

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researchers in all areas of pure and applied mathematics

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