Details of MA4201 (Spring 2021)
| Level: 4 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA4201 | Algebra III | Swarnendu Datta |
| Syllabus |
|---|
| 1. Rings, ideals, quotient rings, homomorphisms and isomorphisms, prime ideals, maximal ideals, integral domains, field of fractions.
2. Modules, submodules, quotient modules, morphisms, tensor product, flat modules. 3. Chain condition. 4. Completion, localization, valuation. 5. Regularity, introduction to dimension theory. |
| Prerequisite |
|---|
| 1. Artin, M., Algebra, Prentice-Hall.
2. Artin, E., Algebra with Galois Theory, Courant Lecture Notes. 3. Gopalkrishnan, N.S., University Algebra, New Age International Press. 4. Lang, S., Algebra, Springer. 5. Morandi, P., Field and Galois Theory, Springer-Verlag |
| References |
|---|
| 1. Artin, M., Algebra, Prentice Hall, 1996.
2. Matsumura, H., Commutative Ring Theory, Cambridge Studies in Advanced Mathematics, 1989. 3. Luthar, I. S. and Passi, I. B. S., Algebra: Volume 2: Rings, Narosa Publishing House, 2008 reprint. 4. Luthar, I. S. and Passi, I. B. S., Algebra: Volume 3: Modules, Narosa Publishing House, 2010 reprint. 5. Eisenbud, D., Commutative Algebra with a view towards Algebraic Geometry, GTM 151, Springer-Verlag, 1995. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Core |
| 3 | IP | 6 | Not Allowed |
| 4 | MR | 2 | Not Allowed |
| 5 | MR | 4 | Not Allowed |
| 6 | MS | 10 | Not Allowed |
| 7 | MS | 4 | Not Allowed |
| 8 | MS | 6 | Not Allowed |
| 9 | MS | 8 | Core |
| 10 | RS | 1 | Elective |
| 11 | RS | 2 | Elective |