Rafiquddin Rafiquddin ; Ayazul Hasan ; Mohammad Fareed Ahmad - [Retracted by the journal] α-modules and generalized submodules

cm:9552 - Communications in Mathematics, July 4, 2019, Volume 27 (2019), Issue 1 - https://doi.org/10.2478/cm-2019-0002
[Retracted by the journal] α-modules and generalized submodulesArticle

Authors: Rafiquddin Rafiquddin 1; Ayazul Hasan ; Mohammad Fareed Ahmad

  • 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[This article has been retracted by the journal ; see Retractation notice https://doi.org/10.2478/cm-2019-0014]A QTAG-module M is an α-module, where α is a limit ordinal, if M/Hβ (M) is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.

Volume: Volume 27 (2019), Issue 1
Published on: July 4, 2019
Imported on: May 11, 2022
Keywords: [MATH]Mathematics [math]


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