| Credit Structure: 2 1 0 6 | Prerequisites : MA 501, MA 509 |
Algebraic numbers and their basic properties, Algebraic number fields and rings of integers, Discriminant of a number field, Unique factorization of ideals in algebraic number fields, Class group and class number, Ramification of primes, Kummer's Theorem, Dedekind's Discriminant Theorem, Cyclotomic fields and Kronecker-Weber theorem (statement only). Introduction to class field theory.
Texts / References
J. W. Cassels, Local Fields, Cambridge University Press, 1986.
H. M. Edwards, Fermat's Last Theorem, Springer-Verlag, 1977.
A. Frohlich and M. J. Taylor, Algebraic Number Theory, Cambridge University Press, 1993.
K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, 2nd ed., Springer-Verlag, 1990.
S. Lang, Algebraic Number Theory, Addison-Wesley, 1970.
D.A. Marcus, Number Fields, Springer-Verlag, 1977.
Apart from these, I shall refer to my Notes, which are available here.