# MA3203 Ring Theory Spring 2024

### Official Course Description

## Course Info

### Meetings

- Monday 10.15-12.00 in R92 in Realfagbygget.
- Thursday 12.15-14.00 in MA24 in Grønnbygget.

The first meeting is Monday, January 8th, and the last meeting is Thursday, May 2nd.

### Lecturer

- Jacob Fjeld Grevstad
- Office: 829, Sentralbygg II
- Office Hours: Just contact me by email!

### Course plan

We will use a flipped classroom for this course. This means that you will watch videos outside of class (produced by Øyvind Solberg) and during class we will solve exercises together. I also plan to give you the opportunity to present your solutions during class. This will be a good preparation for the exam, which is oral.

In order for this approach to be successful you are expected to do the following:

- Watch and try to understand the videos before class.
- Come to class and try to participate actively as much as possible.
- Please inform me by email if you are not able to come to a class.

### Exam

There will be an oral exam.

### Syllabus/Topics Covered

- Quivers, path algebras, and representations of quivers
- Finite length modules
- Radicals of rings and modules
- Projective modules
- Artin algebras
- Categories and functors
- The Krull-Remak-Schmidt Theorem
- Injective modules and socles
- Duality

### Textbooks

Here are some relevant textbooks

- Authors: M. Auslander, I. Reiten, and S. O. Smalø
- Title: Representation theory of Artin algebras, Cambridge studies in mathematics 36
- Publisher: Cambridge University Press
- Edition: Second edition
- Year: 1995
- ISBN: 0-521-59923-7

- Authors: I. Assem, D. Simson, and A. Skowroński
- Title: Elements of the representation theory of associative algebras, vol 1: techniques of representation theory, London Mathematical Society student textss 65
- Publisher: Cambridge University Press
- Edition: First edition
- Year: 2006
- ISBN: 978-0-521-58631-3

- Authors: A. Skowroński, and K. Yamagata
- Title: Frobenius Algebras I: Basic Representation Theory
- Publisher: European Mathematical Society
- Edition: First edition
- Year: 2011
- ISBN: 978-3-03719-102-6

### Reference Group

We will have a reference group for the course