<h3>MA7830 Advanced Algebra</h3>
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<h4>Course Details</h4>
Groups: Basics of groups and its representations.<br>
Commutative Rings: Dimension Theory, Regular local ring is a UFD. Hilbert functions. <br>
Modules: The tensor, symmetric and exterior algebras of a module. <br>
Non-commutative Rings: Review of Artin-Wedderburn theory including theorems of Jacobson-Bourbaki, Rieffel and Burnside, Kolchin's theorem. <br>
Homological Algebra: Categories and Functors, Abelian categories, Projective and Injective resolutions, Left and Right derived functors, Ext and Tor, Local and Cech homology.
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<h4>Course References:</h4>
Text Books:<br>
1.      S. Lang, Algebra, 3rd Edition, Addison-Wesley, 1999.<br>
2.      M. F. Atiyah, I. G. Macdonald, Introduction to Commutative Algebra. Addison-Wesley, 1969.<br>
3.      W. Fulton, J. Harris, Representation Theory - A First Course, GTM, Readings in Mathematics 129. Springer Verlag (1991<br>
Reference:<br>
1.      H. Matsumura, Commutative Ring Theory, Second edition,Cambridge Studies in Advanced Mathematics, 8.Cambridge University Press, Cambride 1989.<br>
2.      H. Matsumura, Commutative Algebra. Second edition. Mathematics Lecture Notes Series 56, Benjamin / Cummings Publishing,1980.<br>
3.      M. Artin, Algebra, Prentice Hall, 1994.<br>