Course content

The course is a continuation of MA3201 Rings and modules. It is mainly concerned with discussing finite dimensional algebras over a field. The content of the course may vary, but the core will consist of representations of quivers, path algebras, artinian, noetherian and local rings, projective and injective modules, the Jordan-Hölder Theorem and the Krull-Remak-Schmidt Theorem, radical and socle of modules and rings, exact sequences, categories, functors, equivalence, and duality.

Learning outcome

1. Knowledge. The student masters the connection between module theory over finite dimensional algebras and representations of quivers. The student has basic knowledge of categories, functors, radical, base, and exact sequences. The student understands the Jordan-Hölder theorem and the Krull-Schmidt theorem.

2. Skills. The student is able to find radicals, bases etc. for special classes of finite dimensional algebras. The student is able to describe the corresponding module if a representation is given, and vice versa. The student is able to find the projective cover of a representation, and to calculate almost exact splitting sequences for given finite dimensional algebras.

Learning methods and activities

Lectures/video lectures and problem sessions.

Recommended previous knowledge

The course is based on MA3201 Rings and modules or equivalent (the course may be taken parallel to MA3202 Galois theory).

Course materials

Auslander, Reiten, Smalø: Representation Theory of Artin algebras.

Credit reductions