MA7830 Advanced Algebra

Course Details

Groups: Basics of groups and its representations.
Commutative Rings: Dimension Theory, Regular local ring is a UFD. Hilbert functions.
Modules: The tensor, symmetric and exterior algebras of a module.
Non-commutative Rings: Review of Artin-Wedderburn theory including theorems of Jacobson-Bourbaki, Rieffel and Burnside, Kolchin's theorem.
Homological Algebra: Categories and Functors, Abelian categories, Projective and Injective resolutions, Left and Right derived functors, Ext and Tor, Local and Cech homology.

Course References:

Text Books:
1. S. Lang, Algebra, 3rd Edition, Addison-Wesley, 1999.
2. M. F. Atiyah, I. G. Macdonald, Introduction to Commutative Algebra. Addison-Wesley, 1969.
3. W. Fulton, J. Harris, Representation Theory - A First Course, GTM, Readings in Mathematics 129. Springer Verlag (1991
1. H. Matsumura, Commutative Ring Theory, Second edition,Cambridge Studies in Advanced Mathematics, 8.Cambridge University Press, Cambride 1989.
2. H. Matsumura, Commutative Algebra. Second edition. Mathematics Lecture Notes Series 56, Benjamin / Cummings Publishing,1980.
3. M. Artin, Algebra, Prentice Hall, 1994.