| Title:
|
$\alpha$-modules and generalized submodules (English) |
| Author:
|
Rafiquddin, Rafiquddin |
| Author:
|
Hasan, Ayazul |
| Author:
|
Ahmad, Mohammad Fareed |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
27 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
13-26 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\omega \leq \alpha \leq \omega _1$ we prove that an $\alpha $-large submodule $L$ of an $\omega _1$-module $M$ is summable if and only if $M$ is summable. (English) |
| Keyword:
|
$\alpha$-modules |
| Keyword:
|
$\alpha$-pure submodules |
| Keyword:
|
$\alpha$-basic submodules |
| Keyword:
|
$\alpha$-large submodules. |
| MSC:
|
16K20 |
| idZBL:
|
Zbl 1464.16013 |
| idMR:
|
MR3977474 |
| . |
| Date available:
|
2019-06-28T14:45:31Z |
| Last updated:
|
2021-11-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147765 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
