| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | FMA623 | MODULES AND RINGS I | Compulsory | 1 | 1 | 6 |
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| Level of Course Unit |
| Second Cycle |
| Objectives of the Course |
| To present the Concepts of Ring and Module theory. To provide students with the supporting knowledge necessary for ring and module theory. |
| Name of Lecturer(s) |
| Assist. Prof. Dr. Yıldıray ÇELİK |
| Learning Outcomes |
| 1 | Students prove theorems related to modules and prime submodules | | 2 | Students can pove isomorphism theorems and learn using them to solve problems | | 3 | Students can define the concepts of ring, deal, quotient ring, can give examples and can prove related theorems | | 4 | Students can give examples of rings and ideals | | 5 | Students learn advanced ring theory. |
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| Mode of Delivery |
| Formal Education |
| Prerequisites and co-requisities |
| None |
| Recommended Optional Programme Components |
| None |
| Course Contents |
| Rings and Subrings,Ideals,Homomorphisms,Isomorphisms,Field of fractions,Unique factorization domains,Prime ideals,Maximal ideals,Primary ideals,Fractions of rings,Prime ideals in noncommutative rings,Nil radical,Prime spectrum of rings,Jacobson radical |
| Weekly Detailed Course Contents |
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| 1 | Rings, Subrings and Ideals | | | | 2 | Ring homomorphisms, Isomorphisms | | | | 3 | quotient rings | | | | 4 | polynomial rings | | | | 5 | Prime ideals, maximal ideals | | | | 6 | Primary ideals | | | | 7 | Basic definitions and theorems on modules | | | | 8 | Midterm exam | | | | 9 | Submodules | | | | 10 | Prime submodul | | | | 11 | maximal submodule | | | | 12 | Primary submodule | | | | 13 | Primary decomposition | | | | 14 | Noetherian rings | | | | 15 | Noetherian modules | | | | 16 | Final exam | | |
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| Recommended or Required Reading |
| 1-Algebra,Hungerdford,Springer,1987. |
| Planned Learning Activities and Teaching Methods |
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| Assessment Methods and Criteria | |
| SUM | 0 | |
| SUM | 0 | | Yarıyıl (Yıl) İçi Etkinlikleri | 40 | | Yarıyıl (Yıl) Sonu Etkinlikleri | 60 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | | None |
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| Workload Calculation |
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| Midterm Examination | 1 | 2 | 2 |
| Final Examination | 1 | 2 | 2 |
| Attending Lectures | 14 | 3 | 42 |
| Practice | 14 | 3 | 42 |
| Self Study | 14 | 5 | 70 |
| Individual Study for Homework Problems | 10 | 2 | 20 |
| Individual Study for Mid term Examination | 7 | 2 | 14 |
| Individual Study for Final Examination | 14 | 2 | 28 |
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| Contribution of Learning Outcomes to Programme Outcomes |
| LO1 | 4 | 4 | 4 | 3 | 3 | 4 | 4 | | LO2 | 4 | 4 | 4 | 3 | 3 | 4 | 4 | | LO3 | 4 | 4 | 3 | 3 | 3 | 3 | 4 | | LO4 | 4 | 4 | 3 | 3 | 3 | 3 | 4 | | LO5 | 4 | 4 | 3 | 3 | 2 | 3 | 4 |
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| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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