Thomas Markwig Commutative Algebra - WS 2016/17
Research Interests
Curriculum Vitae


Lecture: Mo 12:15-14:00, N14
Fr 12:14-14:00, N14
Übungen: Mo 08:15-10:00, S11 (Gruppe 1 - Daniel Hättig)
Di 08:15-10:00, S11 (Gruppe 2 - Daniel Hättig)


  1. Hier können die Ergebnisse der Vorlesungsumfrage eingesehen werden.

  2. The oral exams can be arranged on the following days:
    20.2., 13.-14.3., 6.-7.4.
    When you register for the oral exam, you can choose the period (February, March or April) freely; the exact day among those above and the exact time on the day will be set. In case more days are necessary in a period, I will arrange for more days. In due time I will announce how the registration for the exam is done.
  3. The example classes start in the first week of the lecture period. We will meet in the computer room D2A38 where the computer algebra system Singular will be introduced. This will be very helpful to compute examples. Possible times for this class are:
    • Mo, 17.10., 18-20
    • Tu, 18.10., 17-19
    • We, 19.10., 08-10
    We will decide during the first lecture which of the times we are actually offering.
  4. If you intend to participate in the example classes please register online via:


PDF Dateien: 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 .


There will be no official lecture notes to this lecture. However, you can download here the notes Simon Hampe took during the course a couple of years ago:
Lecture notes by Simon Hampe.

Als weitere Literatur empfehle ich:
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.

Universität TübingenDept. of MathematicsSection AlgebraCAS SINGULAR Campus