Some Properties of Strongly Principally Self-Injective Modules
The idea of generalizing quasi injective by employing a new term is introduced in this paper. The introduction of principally self-injective modules, which are principally self-injective modules. A number of characteristics and characterizations of such modules have been established. In addition, th...
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| Format: | Article |
| Language: | English |
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University of Technology, Baghdad
2022-06-01
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| Series: | Journal of Applied Sciences and Nanotechnology |
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| Online Access: | https://jasn.uotechnology.edu.iq/article_17849_5938cc0800cf2d78c6f34a8820df3ec0.pdf |
| _version_ | 1818555068717203456 |
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| author | Khalid Munshid Mohanad Hamid Jehad Kider |
| author_facet | Khalid Munshid Mohanad Hamid Jehad Kider |
| author_sort | Khalid Munshid |
| collection | DOAJ |
| description | The idea of generalizing quasi injective by employing a new term is introduced in this paper. The introduction of principally self-injective modules, which are principally self-injective modules. A number of characteristics and characterizations of such modules have been established. In addition, the idea of strongly mainly self-pure sub-modules was added, which is similar to strongly primarily self-injective sub-modules. Some characteristics of injective, quasi-injective, principally self-injective, principally injective, absolutely self-pure, absolutely pure, and finitely <em>R</em>-injective modules being lengthened to strongly principally self-injective modules. So, in the present work, some properties are added to the concept in a manner similar to the absolutely self-neatness. The fundamental features of these concepts and their interrelationships are linked to the conceptions of some rings. (Von Neumann) regular, left SF-ring, and left pp-ring rings are described via such concept. For instance, the homomorphic picture of every principally injective module be strongly principally self-injective if <em>R</em> being left pp-ring, and another example for a commutative ring R of every strongly principally self-injective module be flat if <em>R</em> being (Von Neumann) regular. Also, a ring <em>R</em> be (Von Neumann) regular if and only if each <em>R</em>-module being strongly principally self-injective module. |
| first_indexed | 2024-12-12T09:48:23Z |
| format | Article |
| id | doaj.art-c49828a255b24843873646023d24fc11 |
| institution | Directory Open Access Journal |
| issn | 2788-6867 |
| language | English |
| last_indexed | 2024-12-12T09:48:23Z |
| publishDate | 2022-06-01 |
| publisher | University of Technology, Baghdad |
| record_format | Article |
| series | Journal of Applied Sciences and Nanotechnology |
| spelling | doaj.art-c49828a255b24843873646023d24fc112022-12-22T00:28:20ZengUniversity of Technology, BaghdadJournal of Applied Sciences and Nanotechnology2788-68672022-06-012213214110.53293/jasn.2021.3248.109617849Some Properties of Strongly Principally Self-Injective ModulesKhalid Munshid0Mohanad Hamid1Jehad Kider2Department of Applied Sciences, University of Technology – IraqDepartment of Production Engineering and Metallurgy, University of Technology – IraqDepartment of Applied Sciences, University of Technology – IraqThe idea of generalizing quasi injective by employing a new term is introduced in this paper. The introduction of principally self-injective modules, which are principally self-injective modules. A number of characteristics and characterizations of such modules have been established. In addition, the idea of strongly mainly self-pure sub-modules was added, which is similar to strongly primarily self-injective sub-modules. Some characteristics of injective, quasi-injective, principally self-injective, principally injective, absolutely self-pure, absolutely pure, and finitely <em>R</em>-injective modules being lengthened to strongly principally self-injective modules. So, in the present work, some properties are added to the concept in a manner similar to the absolutely self-neatness. The fundamental features of these concepts and their interrelationships are linked to the conceptions of some rings. (Von Neumann) regular, left SF-ring, and left pp-ring rings are described via such concept. For instance, the homomorphic picture of every principally injective module be strongly principally self-injective if <em>R</em> being left pp-ring, and another example for a commutative ring R of every strongly principally self-injective module be flat if <em>R</em> being (Von Neumann) regular. Also, a ring <em>R</em> be (Von Neumann) regular if and only if each <em>R</em>-module being strongly principally self-injective module.https://jasn.uotechnology.edu.iq/article_17849_5938cc0800cf2d78c6f34a8820df3ec0.pdfabsolutely self-pureprincipally self-injectivequasi injectivestrongly principally self-injective |
| spellingShingle | Khalid Munshid Mohanad Hamid Jehad Kider Some Properties of Strongly Principally Self-Injective Modules Journal of Applied Sciences and Nanotechnology absolutely self-pure principally self-injective quasi injective strongly principally self-injective |
| title | Some Properties of Strongly Principally Self-Injective Modules |
| title_full | Some Properties of Strongly Principally Self-Injective Modules |
| title_fullStr | Some Properties of Strongly Principally Self-Injective Modules |
| title_full_unstemmed | Some Properties of Strongly Principally Self-Injective Modules |
| title_short | Some Properties of Strongly Principally Self-Injective Modules |
| title_sort | some properties of strongly principally self injective modules |
| topic | absolutely self-pure principally self-injective quasi injective strongly principally self-injective |
| url | https://jasn.uotechnology.edu.iq/article_17849_5938cc0800cf2d78c6f34a8820df3ec0.pdf |
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