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.