Details of MA3202 (Spring 2025)
| Level: 3 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA3202 | Algebra-II | Md. Ali Zinna |
| Syllabus |
|---|
| Rings and Ideals: Rings and ring homomorphism, ideals, quotient rings, zero-divisors,
units, prime and maximal ideals, nilradical and Jacobson radical operations on ideals, extension and contraction, division in domains, g.c.d. and l.c.m., division algorithm, Euclidean domain, unique factorization domain, principal ideal domain. Modules: Modules and module homomorphisms, submodule and quotient modules, operations on submodules, direct sum and product, finitely generated modules, classification of finitely generated modules over PIDs, exact sequences of modules, tensor product of modules, canonical forms. |
| Prerequisite |
|---|
| Algebra I (MA3102) |
| References |
|---|
| 1. Artin, M., Algebra, Prentice-Hall.
2. Atiyah, M.F. and MacDonald, I.G., Introduction to Commutative Algebra, AddisonWesley. 3. Dummit, D.S. and Foote, R.M., Abstract Algebra, Wiley. 4. Eisenbud, D., Commutative Algebra with a view towards Algebraic Geometry, SpringerVerlag. 5. Gopalakrishnan, N.S., Commutative Algebra, Oxonian Press. 6. Kunz, E., Introduction to Commutative Algebra and Algebraic Geometry, Birkhauser. 7. Luthar, I.S. and Passi, I.B.S., Algebra, Vol. 2: Rings, Narosa Publishing House. 8. Luthar, I.S. and Passi, I.B.S., Algebra, Vol. 3: Modules, Narosa Publishing House. 9. Matsumura, H., Commutative Ring Theory, Cambridge University Press. 10. Reid, M., Undergraduate Commutative Algebra, London Mathematical Society Student Texts (29), Cambridge University Press. 11. Sharp, R.Y., Steps in Commutative Algebra, London Mathematical Society Student Texts (19), Cambridge University Press. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Not Allowed |
| 3 | IP | 6 | Not Allowed |
| 4 | MP | 2 | Core |
| 5 | MP | 4 | Not Allowed |
| 6 | MR | 2 | Not Allowed |
| 7 | MR | 4 | Not Allowed |
| 8 | MS | 10 | Elective |
| 9 | MS | 4 | Not Allowed |
| 10 | MS | 6 | Core |
| 11 | MS | 8 | Elective |
| 12 | RS | 1 | Elective |
| 13 | RS | 2 | Elective |