Rings and Modules(MAT461)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT461 | Rings and Modules | 7 | 3 | 0 | 0 | 3 | 5 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | Turkish |
| Course Type | Elective |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Can Ozan OĞUZ canozanoguz@gmail.com (Email) |
| Assistant | |
| Objective | The main objective is to give an introduction to the theory of rings and that of modules. |
| Content | In this course, we study the general definition of a ring and the morphisms between them, before turning our attention to the important example of the rings of polynomials. Next we discuss the classes of rings that have some additional interesting properties (eg, Euclidean rings, principal rings, and factor rings). We then discuss modules. |
| Course Learning Outcomes | |
| Teaching and Learning Methods | |
| References |
1)Daniel Guin-Algèbre II Anneaux, Modules et Algèbre Multilinéaire 2)Hungerford - Algebra 3)Pierre Antoine Grillet - Abstract Algebra |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Definitions and examples of rings |
| 2 | Rings of polynomials, rings of matrices |
| 3 | Homomorphism of rings, the sub-rings |
| 4 | The ideals and Operations on the ideals |
| 5 | Partial 1 |
| 6 | Quotient rings, prime and maximum ideals |
| 7 | The main ideals |
| 8 | Euclidean rings |
| 9 | Definitions and examples of modules |
| 10 | Partial 2 |
| 11 | Modules, sums and product of modules |
| 12 | Modules on the principal rings, free modules, |
| 13 | Noetherian and Artinian Modules |
| 14 | Projective and Injetive Modules |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 5 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 6 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 5 | 60 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 0 | 0 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 0 | 0 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Toplam | 5 | 60 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Total Workload | 0 | ||
| Total Workload / 25 | 0.00 | ||
| Credits ECTS | 0 | ||