1. bookVolume 27 (2019): Issue 1 (June 2019)
Journal Details
License
Format
Journal
eISSN
2336-1298
First Published
16 Jun 2010
Publication timeframe
2 times per year
Languages
English
access type Open Access

α-modules and generalized submodules

Published Online: 04 Jul 2019
Volume & Issue: Volume 27 (2019) - Issue 1 (June 2019)
Page range: 13 - 26
Received: 02 May 2018
Accepted: 16 Jan 2019
Journal Details
License
Format
Journal
eISSN
2336-1298
First Published
16 Jun 2010
Publication timeframe
2 times per year
Languages
English
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.

Keywords

MSC 2010

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