Different Characterizations of Large Submodules of QTAG-Modules
A module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. The study of large submodules and its fascinating properties makes the theory of QTAG-modules more interesting. A fully invarian...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2017/2496246 |
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| author | Fahad Sikander Alveera Mehdi Sabah A. R. K. Naji |
| author_facet | Fahad Sikander Alveera Mehdi Sabah A. R. K. Naji |
| author_sort | Fahad Sikander |
| collection | DOAJ |
| description | A module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. The study of large submodules and its fascinating properties makes the theory of QTAG-modules more interesting. A fully invariant submodule L of M is large in M if L+B=M, for every basic submodule B of M. The impetus of these efforts lies in the fact that the rings are almost restriction-free. This motivates us to find the necessary and sufficient conditions for a submodule of a QTAG-module to be large and characterize them. Also, we investigate some properties of large submodules shared by Σ-modules, summable modules, σ-summable modules, and so on. |
| format | Article |
| id | doaj-art-b1314aa59d1a4534b38745a46c360ff9 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-b1314aa59d1a4534b38745a46c360ff92025-02-03T05:52:00ZengWileyJournal of Mathematics2314-46292314-47852017-01-01201710.1155/2017/24962462496246Different Characterizations of Large Submodules of QTAG-ModulesFahad Sikander0Alveera Mehdi1Sabah A. R. K. Naji2College of Science and Theoretical Studies, Saudi Electronic University, Jeddah Branch, Jeddah 23442, Saudi ArabiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Al Bayda University, Al Bayda, YemenA module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. The study of large submodules and its fascinating properties makes the theory of QTAG-modules more interesting. A fully invariant submodule L of M is large in M if L+B=M, for every basic submodule B of M. The impetus of these efforts lies in the fact that the rings are almost restriction-free. This motivates us to find the necessary and sufficient conditions for a submodule of a QTAG-module to be large and characterize them. Also, we investigate some properties of large submodules shared by Σ-modules, summable modules, σ-summable modules, and so on.http://dx.doi.org/10.1155/2017/2496246 |
| spellingShingle | Fahad Sikander Alveera Mehdi Sabah A. R. K. Naji Different Characterizations of Large Submodules of QTAG-Modules Journal of Mathematics |
| title | Different Characterizations of Large Submodules of QTAG-Modules |
| title_full | Different Characterizations of Large Submodules of QTAG-Modules |
| title_fullStr | Different Characterizations of Large Submodules of QTAG-Modules |
| title_full_unstemmed | Different Characterizations of Large Submodules of QTAG-Modules |
| title_short | Different Characterizations of Large Submodules of QTAG-Modules |
| title_sort | different characterizations of large submodules of qtag modules |
| url | http://dx.doi.org/10.1155/2017/2496246 |
| work_keys_str_mv | AT fahadsikander differentcharacterizationsoflargesubmodulesofqtagmodules AT alveeramehdi differentcharacterizationsoflargesubmodulesofqtagmodules AT sabaharknaji differentcharacterizationsoflargesubmodulesofqtagmodules |