Lecturer Prof. Paul Nelson	Lectures Tue 15-17, HG D 1.1 Thu 13-15, HG D 1.1
Coordinator Emilio Corso	Exercise classes Mon 15-16, HG D 1.1 Mon 15-16, ML F 36

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Starting dates

First lecture: Tue, September 18, 2018

First exercise classes: Mon, September 24, 2018

This course provides an introduction to commutative algebra as a foundation for and first steps towards algebraic geometry. We shall cover approximately the material from most of the textbook by Atiyah-MacDonald or the first half of the textbook by Bosch.

Topics include:

• Basics about rings, ideals and modules
• Localization
• Primary decomposition
• Integral dependence and valuations
• Noetherian rings
• Completions
• Basic dimension theory

Prerequisites: Algebra I (or a similar introduction to the basic concepts of ring theory).

Objectives and assignments :

Here you find a constantly updated file containing objectives and assignments for the course: "Objectives and assignments"

The new exercise sheet will be posted here on Tuesdays. We expect you to look at the problems over the weekend and to prepare questions for the exercise class on Monday of the following week.

Please note that each exercise sheet contains 6-7 exercises. Written solutions will be provided the day after the deadline for handing them in.

Please hand in your solutions by the following Thursday at 13:00 (so that you have 9 days to solve the exercises) in room HG J68, in the box under the sign corresponding to the course. Please do not forget to write the name of your teaching assistant on each sheet that you hand in. Your solutions will usually be corrected and returned in the following exercise class or, if not collected, returned to the box in HG J68.

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Exercise sheet	Due by	Solutions
Exercise sheet 1	September 27	Solution sheet 1
Exercise sheet 2	October 4	Solution sheet 2
Exercise sheet 3	October 11	Solution sheet 3
Exercise sheet 4	October 18	Solution sheet 4
Exercise sheet 5	October 25	Solution sheet 5
Exercise sheet 6	November 1	Solution sheet 6
Exercise sheet 7	November 8	Solution sheet 7
Exercise sheet 8	November 19	Solution sheet 8
Exercise sheet 9	November 22	Solution sheet 9
Exercise sheet 10	December 3	Solution sheet 10
Exercise sheet 11	December 10	Solution sheet 11
Exercise sheet 12	December 17	Solution sheet 12
Exercise sheet 13	December 21	Solution sheet 13

You can enrol in exercise classes using echo: here.

Time	Room	Assistant	Language
Mo 15-16	HG G 19.1 (*)	Riccardo Ferrario	en
Mo 15-16	HG D 1.1	Waltraud Lederle	en

(*) Except for Monday 29/10/2018, where the exercise class will take place in ML F 36.

Primary Reference:

1. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995)

Secondary Reference:

2. "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald (Addison-Wesley Publ., 1969)

Tertiary References:

3. "Algebraic Geometry and Commutative Algebra" by S. Bosch (Springer 2013)
4. "Commutative ring theory" by H. Matsumura (Cambridge University Press 1989)
5. "Commutative Algebra" by N. Bourbaki (Hermann, Masson, Springer)