Thomas Markwig Commutative Algebra - WS 2009/10
Research Interests
Curriculum Vitae


Lecture: Mo 13:45-15:15, Rm 48-438 and Di 10:00-11:30, Rm 48-438
Exampleclass: Tu 11:45, Rm 48-438 (Simon Hampe)


  1. In Exercise 33b you will need the second uniqueness theorem (see 5.20 in the lecture notes) for the uniqueness claim.
  2. If you intend to participate in the example classes please register online via: The example class takes place on Tuesdays, at 11:45. In case this time turns out to be inconvenient, we will try to find a more suitable time.
  3. 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: Lecture Notes , Transparencies , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 .


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