Thomas Markwig Commutative Algebra - WS 2014/15
Research Interests
Curriculum Vitae


Lecture: Mo+We 11:45-13:15, Rm 48-438
Exampleclass: Th 11:45-13:15, Rm 48-438 (Cornelia Rottner)


  1. Die Prüfungstermine sind jetzt im Prüfungsverwaltungssystem eingetragen und die Prüfungen können bei Frau Bäsell (48-432) angemeldet werden.
  2. The example classes start on Thursday, October 30, 2014. We will meet in the computer room 48-419 where I will introduce the computer algebra system Singular. This will be very helpful to compute examples.
  3. The lecture starts on Monday, October 27, 2014.
  4. 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.
  5. 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