Thomas Markwig Commutative Algebra - WS 2011/12
Research Interests
Curriculum Vitae


Lecture: Mo 15:30-17:00, Rm 48-438 and Di 15:30-17:00, Rm (48-438 or 48-538)
Exampleclass: We 15:30-17:00, Rm 48-438 (Christian Eder)


  1. I would like to remind you that we will have our Tuesday lecture from this week on in room 48-538 (instead of 48-438). This room is larger and it should usually be available on Tuesdays from 3:30 pm to 5 pm, since it is booked for the colloquium. In the unlikely event that the room is not free we will have to move down to 48-438.
  2. There will be an additional lecture on Wednesday, 2/11/, from 17:15 to 18:45 in Room 48-538. This replaces the lecture on the holiday, 1/11.
  3. If you intend to participate in the example classes please register online via: The example class takes place on Wednesdays, at 15:30. In case this time turns out to be inconvenient, we will try to find a more suitable time.
  4. There are lecture notes by Simon Hampe on a large part of the course available. Please let me know if you find any errors or misprints:

Assingments / Notes:

PDF Dateien: 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 .


Michael F. Atiyah, Ian G. MacDonald Introduction to Commutative Algebra, Addison Wesley.
Hideyuki Matsumura, Commutative Ring Theory, CUP.
Hideyuki Matsumura, Commutative Algebra.
David Eisenbud, Commutative Algebra with a View towards Algebraic Geometry, Springer.
Gert-Martin Greuel, Gerhard Pfister, A Singular Introduction to Commutative Algebra, Springer.
Winfried Bruns, Zahlentheorie, Osnabrücker Schriften zur Mathematik.


Rings and ideals, modules, Nakayama lemma, localization, Noetherian and Artinian rings, primary decomposition, Noether normalization and applications (finite and integral extensions, integral closure, dimension, Hilbert's Nullstellensatz), Krull's Principle Ideal Theorem, Dedekind domains.

Univ. of TübingenDept. of MathematicsSection AlgebraCAS SINGULAR