α-modules and generalized submodules-Reference-Cited by-同舟云学术

α-modules and generalized submodules

Published:2019-06-01 Issue:1 Volume:27 Page:13-26
ISSN:2336-1298
Container-title:Communications in Mathematics
language:en
Short-container-title:

Author:

Rafiquddin ¹,Hasan Ayazul²,Ahmad Mohammad Fareed¹

Affiliation:

1. Department of Applied Mathematics, Faculty of Engineering and Technology , Aligarh Muslim University , Aligarh - 202002 , India

2. College of Applied Industrial Technology , Jazan University , Jazan-P.O. Box 2097, Kingdom of Saudi Arabia , E-mail: ayaz.maths@gmail.com

Abstract

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 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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.sciendo.com/pdf/10.2478/cm-2019-0002

Reference17 articles.

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5. [5] A. Hasan: On essentially finitely indecomposable QTAG-modules. Afrika Mat. 27 (1) (2016) 79–85.

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1. Retraction notice;Communications in Mathematics;2019-12-01