Lecturer Prof. Paul Nelson	Lectures Tue 15-17, HG D 1.1 Thu 13-15, HG D 1.1
Coordinator Paul Steinmann	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 19, 2017

First exercise classes: Mon, September 25, 2017

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).

Notes from Prof. Nelson about dimension: "Commutative algebra: some basics on Krull dimension"

Specific references for each topic:

• Basics on rings, modules, localization [A-M, 1-3]
• Noetherian rings and the Nullstellensatz [A-M, 7]
• Primary decomposition [A-M, 4]
• Artin rings [A-M, 8; Bosch, 2.2]
• Krull dimension theory [Bosch, 2.3-2.4; Eisenbud, 8-10 and 13]
• Integral extensions [A-M, 5; Bosch, 3]
• Valuation rings [A-M, 5; Eisenbud, 11.1]

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

Please hand in your solutions by the following Thursday at 13:00 in your assistant's box in HG J68. Your solutions will usually be corrected and returned in the following exercise class or, if not collected, returned to the box in HG J68.

exercise sheet	due by	solutions
Exercise sheet 1	September 28	Solution sheet 1
Exercise sheet 2	October 5	Solution sheet 2
Exercise sheet 3	October 12	Solution sheet 3
Exercise sheet 4	October 19	Solution sheet 4
Exercise sheet 5	October 26	Solution sheet 5
Exercise sheet 6	November 2	Solution sheet 6
Exercise sheet 7	November 9	Solution sheet 7
Exercise sheet 8	November 16	Solution sheet 8
Exercise sheet 9	November 23	Solution sheet 9
Exercise sheet 10	November 30	Solution sheet 10
Exercise sheet 11	December 7	Solution sheet 11
Exercise sheet 12	December 14	Solution sheet 12
Exercise sheet 13	December 21	Solution sheet 13

time	room	assistant	language
Mo 15-16	HG D 1.1	Dante Bonolis	en
Mo 15-16	ML F 36	Seraina Regina Wachter	en

Notes from Prof. Nelson about dimension: "Commutative algebra: some basics on Krull dimension"

Primary Reference:

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

Secondary Reference:

2. "Algebraic Geometry and Commutative Algebra" by S. Bosch (Springer 2013)

Tertiary References:

3. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995)
4. "Commutative ring theory" by H. Matsumura (Cambridge University Press 1989)
5. "Commutative Algebra" by N. Bourbaki (Hermann, Masson, Springer)