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

Target Group
Students with the prerequisites mentioned below.

Prerequisites
? 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.)
? Further literature will be announced in class.

Homepage: Professor Alexander Schmitt