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| MAT7254 | Ring Theory | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Funda KARAÇAL | | Co-Lecturer | Assoc. Prof. Dr. Osman Kazancı | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Ring theory advanced in issues related to research is to provide basic information. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | be acquainted with the notion of module and define and use the finiteness conditions: the Artinian and Noetherian rings and modules. | 1,4 | 1 | | PO - 2 : | familiarize with fundamental constructions in rings: ring of endomorphisms, the Jacobson radical and basic notions as: simple, semi-simple modules, prime ideals. | 1,4 | 1 | | PO - 3 : | understand some simple applications of topology, made in order to cover dense rings of linear transformations (the Jacobson density theorem). | 1,4 | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Simple and Pirimitive Rings, The Jacobson Radical, Semisimple Rings, The Prime Radical, Prime and Semiprime Rings. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Simple (or irreducible) Modules | | | Week 2 | Regular ideals | | | Week 3 | Simple and faithful modüles | | | Week 4 | Pirimitive rings | | | Week 5 | Dense rings | | | Week 6 | Jacobson Density Theorem | | | Week 7 | Wedderburn-Artin Theorem | | | Week 8 | Mid-term exam | | | Week 9 | Jacobson radical | | | Week 10 | Quasi-regular ideals | | | Week 11 | Semisimple rings | | | Week 12 | Nil and Nilpotent ideals | | | Week 13 | Prime radical | | | Week 14 | Prime ideals. | | | Week 15 | Goldie rings | | | Week 16 | End-of-term exam | | | |
| 1 | Hungerford, T. W. 1980 , Algebra, 2nd Edition. Berlin-Heidelberg-New York. | | | |
| 1 | McCoy, N. H. 1973 The theory of rings. New York. Chelsea Publishing Co. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 8 | 30/03/2024 | 2,00 | 30 | | Quiz | 12 | 30/04/2024 | 2,00 | 20 | | End-of-term exam | 16 | 01/06/2024 | 2,00 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 8 | 14 | 112 | | Arasınav için hazırlık | 15 | 1 | 15 | | Arasınav | 2 | 1 | 2 | | Ödev | 10 | 1 | 10 | | Dönem sonu sınavı için hazırlık | 16 | 1 | 16 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 199 |
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