On Rings whose Simple Singular R-Modules are GP-Injective
In this work we give a characterization of rings whose simple singular right R-modules are Gp-injective. We prove that if R is a quasi-duo ring whose simple singular right R-modules are Gp-injective, then any reduced right ideal of R is a direct summand. We also consider that a zero commutative ring...
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| Format: | Article |
| Language: | English |
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Mosul University
2005-06-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
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| Online Access: | https://csmj.mosuljournals.com/article_164068_54a19268a4494fa724423e7d496d4130.pdf |
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| _version_ | 1849727888915431424 |
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| author | Zubayda Ibraheem |
| author_facet | Zubayda Ibraheem |
| author_sort | Zubayda Ibraheem |
| collection | DOAJ |
| description | In this work we give a characterization of rings whose simple singular right R-modules are Gp-injective. We prove that if R is a quasi-duo ring whose simple singular right R-modules are Gp-injective, then any reduced right ideal of R is a direct summand. We also consider that a zero commutative ring with every simple singular left R-module is Gp-injective |
| format | Article |
| id | doaj-art-1ceaee109e1044caa31b934dcf2f5d0d |
| institution | DOAJ |
| issn | 1815-4816 2311-7990 |
| language | English |
| publishDate | 2005-06-01 |
| publisher | Mosul University |
| record_format | Article |
| series | Al-Rafidain Journal of Computer Sciences and Mathematics |
| spelling | doaj-art-1ceaee109e1044caa31b934dcf2f5d0d2025-08-20T03:09:43ZengMosul UniversityAl-Rafidain Journal of Computer Sciences and Mathematics1815-48162311-79902005-06-0121636710.33899/csmj.2005.164068164068On Rings whose Simple Singular R-Modules are GP-InjectiveZubayda Ibraheem0College of Computers Sciences and Mathematics University of Mosul, IraqIn this work we give a characterization of rings whose simple singular right R-modules are Gp-injective. We prove that if R is a quasi-duo ring whose simple singular right R-modules are Gp-injective, then any reduced right ideal of R is a direct summand. We also consider that a zero commutative ring with every simple singular left R-module is Gp-injectivehttps://csmj.mosuljournals.com/article_164068_54a19268a4494fa724423e7d496d4130.pdfgp-injectiver-modulesquasi-duo ringzc-ring |
| spellingShingle | Zubayda Ibraheem On Rings whose Simple Singular R-Modules are GP-Injective Al-Rafidain Journal of Computer Sciences and Mathematics gp-injective r-modules quasi-duo ring zc-ring |
| title | On Rings whose Simple Singular R-Modules are GP-Injective |
| title_full | On Rings whose Simple Singular R-Modules are GP-Injective |
| title_fullStr | On Rings whose Simple Singular R-Modules are GP-Injective |
| title_full_unstemmed | On Rings whose Simple Singular R-Modules are GP-Injective |
| title_short | On Rings whose Simple Singular R-Modules are GP-Injective |
| title_sort | on rings whose simple singular r modules are gp injective |
| topic | gp-injective r-modules quasi-duo ring zc-ring |
| url | https://csmj.mosuljournals.com/article_164068_54a19268a4494fa724423e7d496d4130.pdf |
| work_keys_str_mv | AT zubaydaibraheem onringswhosesimplesingularrmodulesaregpinjective |