S-Generalized supplemented modules
Xue introduced the following concept: Let M be an R- module. M is called a generalized supplemented module if for every submodule N of M, there exists a submodule K of M such that M = N +K and N Ç K Í Rad(K). • Hamada and B. AL- Hashimi introduced the following concept: Let S be a property...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Baghdad, College of Science for Women
2024-10-01
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| Series: | مجلة بغداد للعلوم |
| Subjects: | |
| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/11913 |
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| Summary: | Xue introduced the following concept: Let M be an R- module. M is called a generalized supplemented module if for every submodule N of M, there exists a submodule K of M such that M = N +K and N Ç K Í Rad(K).
• Hamada and B. AL- Hashimi introduced the following concept:
Let S be a property on modules. S is called a quasi – radical property if the following conditions are satisfied:
• For every epimorphism f: M ® N, where M and N are any two R- modules. If the module M has the property S, then the module N has the property S.
• Every module M contained the submodule S(M).
These observations lead us to introduce S- generalized supplemented modules. Let S be a quasi- radical property. We say that an R-module M is S- generalized supplemented module if for every submodule N of M, there exists a submodule K of M such that M = N + K and N Ç K Í S(K).
The main purpose of this work is to develop the properties of S-generalized supplemented modules. Many interesting and useful results are obtained about this concept. We illustrate the concepts, by examples.
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| ISSN: | 2078-8665 2411-7986 |