ALGEBRA - II
Part A
- Introduction to categories and functors, direct and inverse limits;
- Field of fractions of an integral domain, localization of rings;
- I-adic completion of rings;
- Tensor products, short exact sequences of modules;
- Noetherian rings and modules, Hilbert Basis Theorem, Jordan-Holder Theorem;
- Artinian rings, Artinian implies Noetherian, Krull-Schmidt Theorem.
Part B
- Splitting fields, normal and separable extensions;
- Application to finite fields;
- The Fundamental Theorem of Galois Theory;
- The Primitive Element Theorem.
Books
- Artin, M., Algebra, Prentice-Hall of India, 1994.
- Dummit, D. S. and Foote, R. M., Abstract Algebra, John Wiley & Sons, 2001.
- Lang, S., Algebra, 3rd editiom. Springer, 2002.
- Atiyah, M. and MacDonald, R., Introduction to Commutative Algebra, Addison- Wesley(or any reprint).