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MA 213: Algebra II
Prerequisite courses: MA 212
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.
Splitting fields, normal and separable extensions;
Application to finite fields;
The Fundamental Theorem of Galois Theory;
The Primitive Element Theorem.
Suggested books and references:
, Prentice_Hall of India, 1994.
Dummit, D. S. and Foote, R. M.,
, McGraw-Hill, 1986.
Algebra (3rd Ed.)
, Springer, 2002.
Atiyah, M. and MacDonald, R.,
Introduction to Commutative Algebra
, Addison-Wesley(or any reprint).
+91 (80) 2293 2711, +91 (80) 2293 2265 ;
Last updated: 20 Feb 2020