MA7830 Advanced Algebra

Course contents:

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.

 

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).

 

Reference:

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.