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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 | Prof. Dr. Sultan YAMAK | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | This course aims to provide the fundamental information for advanced investigations on the topics related to ring theory. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | The students will explain the chain conditions and the structure of lattices on Artinian and Noetherian rings and modules. | 1,2,3 | 1, | | PO - 2 : | The students will explain the structure of Jacobson radicals and ring endomorphies of simple and semi-simple modules and establish the relationship between them. | 1,2,3 | 1, | | PO - 3 : | The students will comprehend that the ring of linear transformations has applications in topology. | 1,2,3 | 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 modules | | | 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 | Hungerdford, T. W. 1974; Algebra, Springer-Verlag, NewYork | | | |
| 1 | McCoy, N. H. 1973; The Theory of Rings. Chelsea, Bronx, NewYork | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 15/04/2024 | 2 | 30 | | In-term studies (second mid-term exam) | 13 | 13/05/2024 | 2 | 20 | | End-of-term exam | 16 | 01/06/2024 | 2 | 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 | 3 | 14 | 42 | | Arasınav için hazırlık | 10 | 8 | 80 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 9.5 | 6 | 57 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 225 |
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