Commutative Algebra

First lecture: Wednesday., Sep. 18.

First exercise class : Tuesday, Sep. 24 or Thursday, Sep. 26.

Testat conditions: Starting from the autumn semester, there is no testat condition (see here). It is nevertheless strongly recommend to work on the problem sheets and hand them in for correction.  The exercises are useful for understanding the concepts of the course and to hand them in is for your own benefit. They are also important for the exam at the end of the semester.

Content

We shall closely follow the text "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald. Wherever possible, there will be extra focus on exercises that lead towards the basics of Algebraic Geometry. Topics include
* Basics about rings, ideals and modules
* Localisation
* Primary decomposition
* Integral dependence and valuations
* Noetherian rings
* Completions
* Basic dimension theory

Literatur

Basic reference for the course

M. Atiyah, I. Macdonald: Introduction to Commutative Algebra, Addison-Wesley (1969)

D. Eisenbud: Commutative Algebra. With a View Toward Algebraic Geometry, GTM 150, Springer Verlag (1995)

O. Zariski, P. Samuel: Commutative Algebra I, Van Nostrand (1965)

H. Matsumura: Commutative Algebra, Benjamin-Cummings Pub Co (1980).

Exercise groups

Problem Sheets

For comments/questions/corrections to the sheets and solutions please send an email here. You can hand in the solutions to the problem sheets either in the exercise classes or alternatively use the box of your assistant in the printer room HG J 68. There will be solutions to the problems posted some time after the due date.