Details of MA3110 (Autumn 2025)
| Level: 3 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA3110 | Ring Theory | Arjun Paul |
| Syllabus |
|---|
| Rings and Ideals: Rings and ring homomorphism, ideals, quotient rings, zero-
divisors, units, prime and maximal ideals, nilradical and Jacobson radical, opera- tions on ideals, extension and contraction of ideals. Chinese remainder theorem. Division in domains, g.c.d. and l.c.m., division algorithm, Euclidean domain, unique factorization domain, principal ideal domain. Polynomial Rings: Definitions and examples, basic properties, polynomial rings over fields. Irreducibility of polynomials, Eisensteins criterion, Gauss lemma and Gauss theorem, and their applications. |
| Prerequisite |
|---|
| Basic algebra (MA2205) |
| References |
|---|
| Suggested Texts:
(a) Artin, M., Algebra, Prentice-Hall. (b) Dummit, D.S. and Foote, R.M., Abstract Algebra, Wiley. (c) Fraleigh, J.B., A First Course in Abstract Algebra, Narosa Publishers. (d) Gopalakrishnan, N.S., University Algebra, New Age International. (e) Herstein, I.N., Topics in Algebra, Wiley. (f) Hungerford, T.W., Algebra, Springer-Verlag. (g) Malik, D.S., Mordeson, J.M. and Sen, M.K., Fundamentals of Abstract Al-gebra, McGraw-Hill. Reference books (a) Atiyah, M.F. and MacDonald, I.G., Introduction to Commutative Algebra, Addison-Wesley. (b) Eisenbud, D., Commutative Algebra with a view towards Algebraic Geometry, Springer-Verlag. (c) Matsumura, H., Commutative Ring Theory, Cambridge University Press. (d) Reid, M., Undergraduate Commutative Algebra, London Mathematical Society Student Texts (29), Cambridge University Press. (e) Lang, Serge. Algebra. Graduate Text in Mathematics, Springer. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 1 | Not Allowed |
| 2 | IP | 3 | Not Allowed |
| 3 | IP | 5 | Not Allowed |
| 4 | MP | 1 | Core |
| 5 | MP | 3 | Not Allowed |
| 6 | MR | 1 | Not Allowed |
| 7 | MR | 3 | Not Allowed |
| 8 | MS | 3 | Not Allowed |
| 9 | MS | 5 | Core |
| 10 | MS | 7 | Elective |
| 11 | MS | 9 | Elective |
| 12 | RS | 1 | Elective |
| 13 | RS | 2 | Not Allowed |