Die Unterrichtssprache ist vorwiegend Englisch, Fragen dürfen auch auf Deutsch gestellt werden.
Lectures are on Tuesday (8:30-10:00 in IA 1/177) and Thursday (12:15-13:45 in IA 1/75)
The course will be a first lecture course in algebra, it will consist of five parts:
- Group theory: symmetric group, alternating group, classification of finite groups, Sylow theorems, structure of finite groups.
- Ring theory: Integral domains (rings with commutative multiplication, no non-trivial zero divisors),
Euclidean domains, principal ideal domains, unique factorisation (in particular in rings of polynomials), the quotient field of an integral domain - Field extensions: towards subfields or towards fields containing a given field. Simple extensions,
algebraic extensions. Galois theory: fundamental theorem, Galois extensions, solvability. - Module theory: modules over principal ideal domains, simple modules, torsion modules.
Potential further courses:
- Representation theory
- Homological algebra
- Commutative algebra
- Quiver representations
- etc.
- Kursleiter/in: Karin Baur
Semester: WiSe 2026/27