Details of MA3110 (Autumn 2026)
| Level: 3 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA3110 | Rings and Modules | Swarnendu Datta |
| Syllabus |
|---|
| Ring theory: Definitions and examples of rings and their homomorphisms, polynomial rings. Units, zero divisors and nilpotent elements in a ring, integral domains.
Ideals and operations on them, quotient rings, isomorphism theorems, correspondence theorem, prime ideals and maximal ideals, nilradical and Jacobson radical, extension and contraction of ideals. Chinese remainder theorem and its applications. Division in domains, g.c.d. and l.c.m., division algorithm in polynomial rings, Euclidean domain, principal ideal domain and unique factorization domain, prime Irreducibility of polynomials, Gauss lemma, Gauss theorem, Eisensteins criterion for irreducibility of a polynomial and their applications. Module theory: Modules and their homomorphisms, submodule and quotient modules, operations on submodules, direct sum and direct product of modules, free modules, finitely generated modules, Nakayamas lemma, tensor product of modules, exact sequence of modules and flatness (if time permits). |
| Prerequisite |
|---|
| Basic algebra (MA2205) |
| References |
|---|
| Suggested Texts:
1.Artin, M., Algebra, Prentice-Hall. 2.Dummit, D.S. and Foote, R.M., Abstract Algebra, Wiley. 3.Fraleigh, J.B., A First Course in Abstract Algebra, Narosa Publishers. 4.Gopalakrishnan, N.S., University Algebra, New Age International. 5.Hungerford, T.W., Algebra, Springer-Verlag. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 1 | Not Allowed |
| 2 | IP | 3 | Not Allowed |
| 3 | MP ( Mathematical Sciences ) | 1 | Core |
| 4 | MP | 3 | Not Allowed |
| 5 | MR | 1 | Not Allowed |
| 6 | MR | 3 | Not Allowed |
| 7 | MS | 3 | Not Allowed |
| 8 | MS ( Mathematical Sciences ) | 5 | Core |
| 9 | MS | 7 | Elective |
| 10 | MS | 9 | Elective |
| 11 | RS | 1 | Elective |
| 12 | RS | 2 | Not Allowed |