Basic Information

This course is a fundamental course for the specialization Algebra/Number theory. In the Bachelor year, it is now possible to take this course instead of taking the course Elemente der Algebra.

An overview of the topics

Group theory

  • Permutation groups
  • Linear groups and representations
  • Quotient groups and composition series

Fields and Galois theory

  • Algebraic and transcendental field extensions
  • Galois theory
  • Finite fields
  • Solving equations using radicals

Ring theory

  • Divisibility and ideals
  • Principal ideal domains and unique factorization domains
  • Hilbert’s basis theorem
  • Hilbert’s Nullstellensatz


  • Representing finitely generated modules with generators and relations
  • Finitely generated modules over principal ideal domains
  • Locally free modules


  • Linear Algebra 1+2


Target Group and Exam Relevance

Algebra is a 4+2 course, which can be taken to earn 9LP.


In the Bachelor, it is possible to take this course instead of taking Elemente der Algebra (4LP). In this case the additional 5LP will count towards the compulsory credits needed for the Wahlpflichtmodul Reine Mathematik


In the Masters of Mathematik, Wirtschaftsmathematik and mathematische Biometrie you can take this lecture as as a Wahlpflichtmodul Reine Mathematik.


In the PO GymPO1 and in the Master Lehramt Mathematik this course can be chosen as a Wahlmodul.


Vorleistung: You will need 50% of the exercise points in order to take the exam.

Exam: There will be an oral exam.




  • Lectures - starting October 15, 2018
  • Monday, 12h-14h, Helmholtzstraße 18,Room 1.20
  • Tuesday, 10h-12h, Helmholtzstraße 18, Room 1.20
  • Exercise sessions- starting October 25, 2018
  • Thursday, 14h-16h Helmholtzstraße 18, E.60

Important Links

The exercise sheets and the lecture notes can be found on Moodle.


  • Bouw/Wewers: Algebra (Master), lecture notes. Will be made available on Moodle.
  • Artin: Algebra
  • Bosch: Algebra.
  • Dummit-Foote, Algebra.
  • Lang: Algebra