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Commutative Algebra (Large Specialization Module)
(dt. Kommutative Algebra (Großes Vertiefungsmodul))

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination (individual examination)
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
One semester,
Person in charge of the module's outline Prof. Dr. Volkmar Welker, Prof. Dr. Sönke Rollenske


Basic algebraic or homological invariants of commutative rings are introduced. Methods for their analysis and their behaviour under classical ring constructions are investigated. Central results of the theory of commutative rings are presented.

Qualification Goals

Students will

  • grasp the basic properties of commutative rings,
  • can apply algebraic or homological methods to analyze commutative rings,
  • understand construction methods of commutative rings and can apply them.
  • have deepened mathematical working methods (development of mathematical intuition and its formal justification, abstraction, proof),
  • have improved their oral communication skills through discussion and free speech in front of an audience in the exercises.


None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, either Algebra [Bachelor Module] or Algebra [Lehramt Module].


Module imported from M.Sc. Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • LAaG Mathematics

When studying B.Sc. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.

Recommended Reading

  • M. Atiyah, I.G. Macdonald, Introduction to commutative algebra, Addison-Wesley, 1994.
  • D. Eisenbud, Commutative Algebra with a view toward algebraic geometry, Springer, 1995.

Please note:

This page describes a module according to the latest valid module guide in Winter semester 2023/24. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.