Details of MA3203 (Spring 2015)

Level: 6 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA3203 Algebra II Shibananda Biswas

Syllabus

  • Definition of rings, group of units, integral domains, fields.

  • Polynomial rings, homomorphisms, ideals, quotients, division algorithm.

  • Factorization in domains, Euclidean Domain, Unique Factorization Domain, Principal Ideal Domain.

  • Integral extensions, primes in integral extensions.

  • Field extensions, algebraic extensions, degree of an extension.

  • Splitting fields, normal extensions, separable extensions.

  • Galois Theory: Galois extensions, automorphism groups and fixed fields, fundamental theorem of Galois theory and applications, cyclic extensions, cyclotomic polynomials, solvability by radicals, constructibility of regular polygons.

References

  1. M. Artin, Algebra, Prentice Hall, 1996.

  2. N. S. Gopalkrishnan, University Algebra, New Age International Press, 1998.

  3. S. Lang, Algebra, GTM 211, Springer-Verlag, 2002.

  4. E. Artin, Algebra with Galois Theory, Courant Lecture Notes, 2007.

  5. P. Morandi, Field and Galois Theory, Springer-Verlag, 1996.

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 2 Core
2 IP 4 Not Allowed
3 MR 2 Not Allowed
4 MR 4 Not Allowed
5 MS 6 Core
6 RS 1 Elective
7 RS 2 Not Allowed