# Lecture class Commutative Algebra (Summer 2023)

The topic of the course is commutative algebra, that is the study of commutative rings and modules over them. This is one of the foundations of modern algebraic geometry and therefore, indirectly, also for algebraic number theory. We will take the connection with algebraic geometry into account right from the start, so that the course provides a natural path into this exciting field, which is one of the most active ones in today’s mathematics.

**Lectures:** Mon, 12-2pm, Tue, 2-4pm, N-U-4.04, first meeting: April 3.

**Exercise group:** (Dr. H. Zhao) Wed, 10am-12pm, N-U-4.04, first meeting: April 12.

**Moodle page for the class:** https://moodle.uni-due.de/course/view.php?id=39589 Password: a2-sommer23

**Literature:**

The content of the course will be more or less the same as in my lecture course on commutative algebra in the summer term 2022, see the lecture notes for that class: pdf , html .

- Atiyah, MacDonald, Introduction to Commutative Algebra
- Matsumura, Commutative Algebra
- Matsumura, Commutative Ring Theory
- Eisenbud, Commutative Algebra with a view towards algebraic geometry
- Bourbaki, Algèbre commutative (or in English: Commutative Algebra)

Further reading:

- K. Conrad, Tensor products (detailed notes on the notion of tensor product, including a discussion on the relation to the notion of tensor which is used in physics)

For further motivation for the curious:

- Görtz, Wedhorn, Algebraic Geometry I. Schemes, with examples and exercises, Vieweg-Teubner, 2010
- U. Görtz, Classics revisited: EGA, Survey paper on Grothendieck’s algebraic geometry, submitted to Jahresbericht der DMV.

**Contact:** Prof. Dr. Ulrich Görtz, ulrich.goertz@uni-due.de