Details of MA3203 (Spring 2020)
| Level: 3 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA3203 | Algebra II | Md. Ali Zinna |
| Syllabus |
|---|
| Rings: Rings, group of units, integral domains, fields, polynomial ring, quotient rings, ideals in quotient ring, ring homomorphisms, isomorphism theorems, prime ideals, maximal ideals, division in domains, g.c.d. and l.c.m., division algorithm, Euclidean domain, unique factorization domain, principal ideal domain.
Fields: Fields, field of fractions, field extensions, algebraic extensions, degree of an extension, splitting fields, normal extensions, separable extensions, finite fields. Galois Theory: Galois extensions, automorphism groups and fixed fields, fundamental theorem of Galois theory and applications, cyclic extensions, cyclotomic polynomials, solvable groups, solvability by radicals, constructibility of regular polygons, transcendental extensions. |
| 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 |
|---|
|
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Core |
| 2 | IP | 4 | Not Allowed |
| 3 | IP | 6 | Not Allowed |
| 4 | MR | 2 | Not Allowed |
| 5 | MR | 4 | Not Allowed |
| 6 | MS | 6 | Core |
| 7 | RS | 1 | Not Allowed |
| 8 | RS | 2 | Not Allowed |