Content:
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
Prerequisites:
Students with the prerequisites mentioned below.
● Linear Algebra I+II ● Algebra and Number Theory

Literature:

• 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.)
• Bosch, S.: Algebraic Geometry and Commutative Algebra, Universitext Springer, 2012.
• Further literature will be announced in class.
  Homepage: Prof. Dr. Dr. h. c. Hélène Esnault