On totally projective QTAG-modules characterized by its submodules
A $QTAG$-module $M$ is called almost totally projective if it has a weak nice system. Here we show that the isotype submodules of a totally projective module which are almost totally projective are precisely those that are separable. From this characterization it follows that every balanced submodul...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2018-10-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/32960 |
| _version_ | 1797633528133844992 |
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| author | Ayazul Hasan Mohd Rafiquddin |
| author_facet | Ayazul Hasan Mohd Rafiquddin |
| author_sort | Ayazul Hasan |
| collection | DOAJ |
| description | A $QTAG$-module $M$ is called almost totally projective if it has a weak nice system. Here we show that the isotype submodules of a totally projective module which are almost totally projective are precisely those that are separable. From this characterization it follows that every balanced submodule of a totally projective module is almost totally projective. Finally, in some special cases we settle the question of whether a direct summand of an almost totally projective module is again almost totally projective. |
| first_indexed | 2024-03-11T11:55:11Z |
| format | Article |
| id | doaj.art-d40c03d6fe9d4284b3423c3e880d8d71 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T11:55:11Z |
| publishDate | 2018-10-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-d40c03d6fe9d4284b3423c3e880d8d712023-11-08T20:09:59ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882018-10-0136410.5269/bspm.v36i4.3296015687On totally projective QTAG-modules characterized by its submodulesAyazul Hasan0Mohd Rafiquddin1Jazan University, JazanAligarh Muslim UniversityA $QTAG$-module $M$ is called almost totally projective if it has a weak nice system. Here we show that the isotype submodules of a totally projective module which are almost totally projective are precisely those that are separable. From this characterization it follows that every balanced submodule of a totally projective module is almost totally projective. Finally, in some special cases we settle the question of whether a direct summand of an almost totally projective module is again almost totally projective.https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/32960totally projective modulesalmost totally projective modulesisotype submodulesseparable submodules |
| spellingShingle | Ayazul Hasan Mohd Rafiquddin On totally projective QTAG-modules characterized by its submodules Boletim da Sociedade Paranaense de Matemática totally projective modules almost totally projective modules isotype submodules separable submodules |
| title | On totally projective QTAG-modules characterized by its submodules |
| title_full | On totally projective QTAG-modules characterized by its submodules |
| title_fullStr | On totally projective QTAG-modules characterized by its submodules |
| title_full_unstemmed | On totally projective QTAG-modules characterized by its submodules |
| title_short | On totally projective QTAG-modules characterized by its submodules |
| title_sort | on totally projective qtag modules characterized by its submodules |
| topic | totally projective modules almost totally projective modules isotype submodules separable submodules |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/32960 |
| work_keys_str_mv | AT ayazulhasan ontotallyprojectiveqtagmodulescharacterizedbyitssubmodules AT mohdrafiquddin ontotallyprojectiveqtagmodulescharacterizedbyitssubmodules |