Derivations of differentially prime rings
| मुख्य लेखक: | |
|---|---|
| स्वरूप: | थीसिस |
| भाषा: | अंग्रेज़ी |
| प्रकाशित: |
2024
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| विषय: | |
| ऑनलाइन पहुंच: | https://ir.upsi.edu.my/detailsg.php?det=12110 |
| Abstract | Abstract here |
| _version_ | 1855626292547813376 |
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| author | Iman Ahmad Taha |
| author_facet | Iman Ahmad Taha |
| author_sort | Iman Ahmad Taha |
| description | |
| format | Thesis |
| id | upsi-12110 |
| institution | Universiti Pendidikan Sultan Idris |
| language | English |
| publishDate | 2024 |
| record_format | sWADAH |
| record_pdf | Restricted |
| spelling | upsi-121102025-04-15 Derivations of differentially prime rings 2024 Iman Ahmad Taha QA Mathematics <p>The concept of derivation on rings is an old problem and plays a very important role in algebra,</p><p>analysis, geometry and physics. The concept of derivation was generalized in different directions</p><p>as centralizing derivation, Lie and Jordan derivations, (, )- derivation, generalized derivations</p><p>and reverse derivations. The main aim of this research is to generalize these concepts. Therefore,</p><p>the action of (, )- derivations on Lie and Jordan Ideals of prime rings with characteristic not</p><p>equal two will be investigated. The next objective was to determine the commutativity of a prime</p><p>ring when the generalized derivation acting on the Jordan ideal of a prime ring. Furthermore, this</p><p>research will extend the centralizing derivations and reverse derivation on - ideal for - prime</p><p>rings. Finally, we extended the concepts of generalized reverse derivation and generalized reverse</p><p>(, )- derivation on a - prime and - semiprime rings. Some techniques and methods of the theory</p><p>of commutative rings will be significantly used in this research, such as the properties of</p><p>commutators and centralizing derivations. The findings of the research showed that the prime ring,</p><p>R is commutative if there is a generalized derivation with a specific condition on R. Also, some</p><p>results depending on a generalized (, )- derivation on Jordan ideal of R are extended. Beside,</p><p>the relationship between some kinds of derivations as centralizing - derivations and the</p><p>commutativity of - prime rings was developed. Finally, the commutativity of - prime ring with</p><p>centralizing reverse - derivation was obtained. It can be concluded that the study of derivation</p><p>and reverse derivation on a prime and - prime rings have considered some conditions to obtain the</p><p>proven results. As an implication, the obtained results in this research can be used as a guide for</p><p>other researchers to extend new results related to semiprime rings in the future.</p><p></p> 2024 thesis https://ir.upsi.edu.my/detailsg.php?det=12110 https://ir.upsi.edu.my/detailsg.php?det=12110 text eng N/A openAccess Doctoral Perpustakaan Tuanku Bainun Fakulti Sains dan Matematik <p>Aboubakr, A. &Gonzalez,S.(2015).GeneralizedReverseDerivationsonSemiprime</p><p>Rings. SiberianMathematicalJournal, 56(2), 199205.</p><p></p><p>Ali, A.&Shah,T.(2008).Centralizingandcommutinggeneralizedderivationson</p><p>prime rings. Matematiki Vesnik, 60(231), 12</p><p></p><p>Al Khalaf,A.D.,Artemovych,O.D&Taha,I.(2018).Derivationsindifferentially</p><p>prime rings. 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| spellingShingle | QA Mathematics Iman Ahmad Taha Derivations of differentially prime rings |
| thesis_level | PhD |
| title | Derivations of differentially prime rings |
| title_full | Derivations of differentially prime rings |
| title_fullStr | Derivations of differentially prime rings |
| title_full_unstemmed | Derivations of differentially prime rings |
| title_short | Derivations of differentially prime rings |
| title_sort | derivations of differentially prime rings |
| topic | QA Mathematics |
| url | https://ir.upsi.edu.my/detailsg.php?det=12110 |
| work_keys_str_mv | AT imanahmadtaha derivationsofdifferentiallyprimerings |