α -modules and generalized submodules

Rafiquddin Rafiquddin; Ayazul Hasan; Mohammad Fareed Ahmad

Communications in Mathematics (2019)

  • Volume: 27, Issue: 1, page 13-26
  • ISSN: 1804-1388

Abstract

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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 ≤ 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.

How to cite

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Rafiquddin, Rafiquddin, Hasan, Ayazul, and Ahmad, Mohammad Fareed. "$\alpha $-modules and generalized submodules." Communications in Mathematics 27.1 (2019): 13-26. <http://eudml.org/doc/294448>.

@article{Rafiquddin2019,
abstract = {A QTAG-module $M$ is an $\alpha $-module, where $\alpha $ is a limit ordinal, if $M/H_\beta (M)$ is totally projective for every ordinal $\beta < \alpha $. In the present paper $\alpha $-modules are studied with the help of $\alpha $-pure submodules, $\alpha $-basic submodules, and $\alpha $-large submodules. It is found that an $\alpha $-closed $\alpha $-module is an $\alpha $-injective. For any ordinal $\omega \le \alpha \le \omega _1$ we prove that an $\alpha $-large submodule $L$ of an $\omega _1$-module $M$ is summable if and only if $M$ is summable.},
author = {Rafiquddin, Rafiquddin, Hasan, Ayazul, Ahmad, Mohammad Fareed},
journal = {Communications in Mathematics},
keywords = {$\alpha $-modules; $\alpha $-pure submodules; $\alpha $-basic submodules; $\alpha $-large submodules},
language = {eng},
number = {1},
pages = {13-26},
publisher = {University of Ostrava},
title = {$\alpha $-modules and generalized submodules},
url = {http://eudml.org/doc/294448},
volume = {27},
year = {2019},
}

TY - JOUR
AU - Rafiquddin, Rafiquddin
AU - Hasan, Ayazul
AU - Ahmad, Mohammad Fareed
TI - $\alpha $-modules and generalized submodules
JO - Communications in Mathematics
PY - 2019
PB - University of Ostrava
VL - 27
IS - 1
SP - 13
EP - 26
AB - A QTAG-module $M$ is an $\alpha $-module, where $\alpha $ is a limit ordinal, if $M/H_\beta (M)$ is totally projective for every ordinal $\beta < \alpha $. In the present paper $\alpha $-modules are studied with the help of $\alpha $-pure submodules, $\alpha $-basic submodules, and $\alpha $-large submodules. It is found that an $\alpha $-closed $\alpha $-module is an $\alpha $-injective. For any ordinal $\omega \le \alpha \le \omega _1$ we prove that an $\alpha $-large submodule $L$ of an $\omega _1$-module $M$ is summable if and only if $M$ is summable.
LA - eng
KW - $\alpha $-modules; $\alpha $-pure submodules; $\alpha $-basic submodules; $\alpha $-large submodules
UR - http://eudml.org/doc/294448
ER -

References

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