| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | 170300401805 | MODULE THEORY | Elective | 4 | 8 | 6 |
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| Level of Course Unit |
| First Cycle |
| Objectives of the Course |
| The aim of this course is to introduce the concepts and algebraic structures related to ring and module theory and to give examples. |
| Name of Lecturer(s) |
| Dr. Öğr. Üyesi Ezgi AYDEMİR |
| Learning Outcomes |
| 1 | Knows the basic concepts of module theory. | | 2 | Has knowledge of homomorphisms and complete sequences. | | 3 | Knows the basic information about finite generator modules. | | 4 | Knows the basic properties of free modules and vector spaces. | | 5 | Has knowledge about Projective and Injective Modules. | | 6 | It uses its knowledge of modules on the main ideal region. |
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| Mode of Delivery |
| Daytime Class |
| Prerequisites and co-requisities |
| - |
| Recommended Optional Programme Components |
| - |
| Course Contents |
| Modules, module homomorphisms and factor modules. Direct sum of modules. Some special module classes. Finitely generated modules. Free modules and submodules of free modules. Decomposition theorems. Prime decomposition of a module. |
| Weekly Detailed Course Contents |
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| 1 | Module definition and examples. | | | | 2 | Module homomorfizmleri and full arrays | | | | 3 | Module homomorfizmleri and full arrays | | | | 4 | Factor modules | | | | 5 | Free Modules and Vector Spaces | | | | 6 | Free Modules and Vector Spaces | | | | 7 | Submodules of free modules | | | | 8 | Midterm exam | | | | 9 | Finitely generated modules | | | | 10 | Direct sum of modules | | | | 11 | Tensor products and applications | | | | 12 | Rings and structure of modules | | | | 13 | Essential ıdeal region on modules | | | | 14 | Decomposition theorems. | | | | 15 | Prime decomposition of a module | | |
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| Recommended or Required Reading |
| T. W. Hungerford, Algebra, Holt, Rinehart and Winston, 1974 J. S. Golan and T. Head, Modules and the structure of rings, Marcel Dekker, 1991 Rings and Modules, Paulo Ribenboim |
| Planned Learning Activities and Teaching Methods |
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| Assessment Methods and Criteria | |
| Midterm Examination | 1 | 70 | | Homework | 1 | 30 | | SUM | 100 | |
| Final Examination | 1 | 100 | | SUM | 100 | | Term (or Year) Learning Activities | 50 | | End Of Term (or Year) Learning Activities | 50 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | | - |
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| Workload Calculation |
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| Midterm Examination | 1 | 1 | 1 |
| Final Examination | 1 | 2 | 2 |
| Attending Lectures | 14 | 2 | 28 |
| Question-Answer | 14 | 3 | 42 |
| Brain Storming | 14 | 2 | 28 |
| Self Study | 14 | 1.5 | 21 |
| Individual Study for Mid term Examination | 1 | 15 | 15 |
| Individual Study for Final Examination | 1 | 20 | 20 |
| Homework | 1 | 20 | 20 |
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| Contribution of Learning Outcomes to Programme Outcomes |
| LO1 | 4 | 3 | 3 | 4 | 4 | 3 | 3 | 3 | 3 | 3 | | LO2 | 4 | 3 | 3 | 4 | 4 | 3 | 3 | 3 | 3 | 3 | | LO3 | 4 | 3 | 3 | 3 | 4 | 3 | 3 | 3 | 3 | 3 | | LO4 | 4 | 3 | 3 | 3 | 4 | 3 | 3 | 3 | 3 | 3 | | LO5 | 4 | 3 | 3 | 3 | 4 | 3 | 3 | 3 | 3 | 3 | | LO6 | 4 | 4 | 4 | 4 | 5 | 4 | 3 | 3 | 4 | 4 |
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| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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Iğdır University, Iğdır / TURKEY • Tel (pbx): +90 476
226 13 14 • e-mail: info@igdir.edu.tr
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