Essentially Retractable Modules
We call a module essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i) A non-zero module is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular module...
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| Language: | English |
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University of Tehran
2007-12-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
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| Online Access: | https://jsciences.ut.ac.ir/article_35080_daa38f2a160fc3e3a8b0aafa70c41eff.pdf |
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| author | M.R. Vedadi |
| author_facet | M.R. Vedadi |
| author_sort | M.R. Vedadi |
| collection | DOAJ |
| description | We call a module essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i) A non-zero module is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii) A non-zero module is essentially retractable if and only if there exists a prime ideal such that HomR. Over semiprime right nonsingular rings, a nonsingular essentially retractable module is precisely a module with non-zero dual. Moreover, over certain rings R, including right FBN rings, it is shown that a nonsingular module M with enough uniforms is essentially retractable if and only if there exist uniform retractable R-modules and R-homomorphisms with . |
| format | Article |
| id | doaj-art-da4d506df78d4ce88775f3273b84787d |
| institution | OA Journals |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2007-12-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-da4d506df78d4ce88775f3273b84787d2025-08-20T01:53:08ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142007-12-0118435536035080Essentially Retractable ModulesM.R. Vedadi0Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Islamic Republic of IranWe call a module essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i) A non-zero module is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii) A non-zero module is essentially retractable if and only if there exists a prime ideal such that HomR. Over semiprime right nonsingular rings, a nonsingular essentially retractable module is precisely a module with non-zero dual. Moreover, over certain rings R, including right FBN rings, it is shown that a nonsingular module M with enough uniforms is essentially retractable if and only if there exist uniform retractable R-modules and R-homomorphisms with .https://jsciences.ut.ac.ir/article_35080_daa38f2a160fc3e3a8b0aafa70c41eff.pdfdual moduleessentially retractablehomo-related |
| spellingShingle | M.R. Vedadi Essentially Retractable Modules Journal of Sciences, Islamic Republic of Iran dual module essentially retractable homo-related |
| title | Essentially Retractable Modules |
| title_full | Essentially Retractable Modules |
| title_fullStr | Essentially Retractable Modules |
| title_full_unstemmed | Essentially Retractable Modules |
| title_short | Essentially Retractable Modules |
| title_sort | essentially retractable modules |
| topic | dual module essentially retractable homo-related |
| url | https://jsciences.ut.ac.ir/article_35080_daa38f2a160fc3e3a8b0aafa70c41eff.pdf |
| work_keys_str_mv | AT mrvedadi essentiallyretractablemodules |