We will mostly use Algebra by Serge Lang. Other books that can be
consulted include, but are certainly not limited to, Introduction to Commutative Algebra by Atiyah and Macdonald, Commutative ring theory by Matsumura and Commutative algebra with a view towards algebraic geometry by Eisenbud. In addition, the notes on Galois theory for finite etale K-algebras might
prove useful.
Contents
Topics include modules (examing the category of left R-modules, tensor
products, hom-functor, etc) with applications to e.g. linear algebra,
commutative ring theory (localization, Hilbert basis theorem, etc.), an
introduction to homological algebra (projective/injective modules, Tor, Ext,
etc.). We will pick additional topics upon interest of the participants.
Grading
Your grade is based on the homework and a (take home) final or presentation.
Click here for
the final. The solutions need to be handed in before May 14, noon.