This is the first part of a three semester course on algebraic geometry. Commutative algebra is the theory of commutative rings and their modules. It formally includes affine algebraic and local analytic geometry. Topics include:
- Affine algebraic varieties
- Rings, ideals, and modules
- Noetherian rings
- Local rings and localization
- Primary decompositione
- Finite and integral extensions
- Dimension theory
- Regular rings
Students with the prerequisites mentioned below.
- Linear Algebra I+II
- Algebra and Number Theory
- Atiyah, M.F.; Macdonald, I.G.: Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969 ix+128 pp. (This book is probably the best entry to the subject. It is short, concise, and clearly written.)
- Further literature will be announced in class.
Homepage: Prof. Altmann