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, 10-12; Wed, 14-16; Place: S-U-3.01; First lecture: April, 9.

Exercise group: Mon, 12-14, Place: O-3.46, First meeting: April, 16.

Notes on the course: pdf (in German, updated on July 16)


  • 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,

Problem sheets

Due date
Sheet 1 pdf April 23
Sheet 2 pdf April 30
Sheet 3 pdf May 7
Sheet 4 pdf May 14
Sheet 5 pdf May 23
Sheet 6 pdf May 28
Sheet 7 pdf June 4
Sheet 8 pdf June 11
Sheet 9 pdf June 18
Sheet 10 (corrected version, June 29) pdf June 25
Sheet 11 pdf July 2
Sheet 12 pdf July 9