| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | FMA624 | MODULES AND RINGS II | Compulsory | 1 | 2 | 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 |
| Weekly Detailed Course Contents |
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| 1 | Rings and Subrings
| | | | 2 | Ideals
| | | | 3 | Homomorphisms
| | | | 4 | Isomorphisms
| | | | 5 | Field of fractions
| | | | 6 | Unique factorization domains
| | | | 7 | Prime ideals
| | | | 8 | Midterm exam
| | | | 9 | Maximal ideals
| | | | 10 | Primary ideals
| | | | 11 | Fractions of rings
| | | | 12 | Prime ideals in noncommutative rings
| | | | 13 | Nil radical
| | | | 14 | Prime spectrum of rings
| | | | 15 | Final week | | | | 16 | Final week | | |
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| Recommended or Required Reading |
| 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 | 2 | 28 |
| Practice | 14 | 2 | 28 |
| Problem Solving | 14 | 2 | 28 |
| Self Study | 14 | 3 | 42 |
| 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 | 3 | 3 | 3 | 3 | 3 | 4 | | LO2 | 4 | 3 | 3 | 3 | 3 | 3 | 4 | | LO3 | 4 | 4 | 4 | 3 | 3 | 4 | 4 | | LO4 | 4 | 4 | 3 | 3 | 3 | 3 | 3 | | LO5 | 4 | 3 | 4 | 3 | 3 | 4 | 3 |
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| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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