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(dt. Algebra)

Level, degree of commitment Advanced 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 B.Sc. Mathematics.
One semester,
each winter semester
Person in charge of the module's outline Prof. Dr. Thomas Bauer, Prof. Dr. István Heckenberger, Prof. Dr. Sönke Rollenske, Prof. Dr. Volkmar Welker


Elementary theory of groups and rings. Basic statements about the structure of subgroups and ideals. Constructions of groups and rings (e.g., quotient structures). Special classes of groups and rings and their theory (e.g., Abelian groups, factorials, and Euclidean rings). Relations to number theory or algebraic geometry. Beginnings of the theory of bodies.

Qualification Goals

Students will be able to,

  • understand basic principles of elementary algebraic objects,
  • derive simple properties of axiomatically defined algebraic structures,
  • recognize algebraic structures in other mathematical areas.
  • proceed according to mathematical working methods (development of mathematical intuition and its formal justification, abstraction, proof),
  • can speak freely about scientific content, both in front of an audience and in a discussion.


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.


Module imported from B.Sc. Mathematics.

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

  • B.Sc. Mathematics
  • M.Sc. Computer Science
  • BA Minor Mathematics

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

The module is assigned to variant A of the BSc minor program in Mathematics.

Recommended Reading

  • M. Artin, Algebra, Birkhäuser, 1993.
  • S. Bosch, Algebra, 8. Aufl., Springer, 2013.
  • G. Fischer, Lehrbuch der Algebra, 3. Aufl,, Spektrum 2013.
  • S. Lang, Algebra, Addison-Wesley, 1984.

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:

  • Winter 2016/17 (no corresponding element)
  • Summer 2018 (no corresponding element)
  • Winter 2018/19 (no corresponding element)
  • Winter 2019/20 (no corresponding element)
  • Winter 2020/21 (no corresponding element)
  • Summer 2021 (no corresponding element)
  • Winter 2021/22 (no corresponding element)
  • Winter 2022/23
  • Winter 2023/24

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.