Syllabus: Number fields and number rings, prime
decomposition in number rings, Dedekind domains, definition of the ideal
class group, Galois theory applied to prime
decomposition and Hilbert ramification theory, Gauss reciprocity law,
Cyclotomic fields and their ring of integers as an example, the
finiteness of the ideal class group,
Dirichlet Unit theorem.
Reference Texts:
1. D. Marcus: Number fields
2. G. J. Janusz: Algebraic Number Theory
https://www.isibang.ac.in/~adean/infsys/database/Bmath/AlgNT.html
- Teacher: Ramesh Sreekantan