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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).
Contact
:
+91 (80) 2293 2711, +91 (80) 2293 2265 ;
E-mail:
chair.math[at]iisc[dot]ac[dot]in
Last updated: 01 Mar 2021