# MA 3203 Ring Theory Spring 2022

From January 27th we will start meeting on campus. Note that we will be in Room KJL2 in Kjelhuset on Thursday 27.01 and S8 in Sentralbygget on Friday 28.01. After that, for the rest of the semester we are supposed to be in K26 in IT-bygget on Thursdays and in R93 in Realfagsbygget on Fridays.

The first meeting is this Thursday 13/01 on Zoom.

Welcome to the Ring theory course!

- Note that the first two weeks of the course (at least) will be held online, and it is not yet clear when we can go back to in-person meetings. If you are planning to attend the course send me an email at sondre [dot] kvamme [at] ntnu [dot] no so that I can compile a email-list for announcements and information.

### Official Course Description

## Course Info

Here is a short Summary of some of the main results covered in the course (it is not supposed to be exhaustive). Remember that during the exam you might also be asked to do some computations, and give proofs of some of the simpler statements. Let me know if you find some errors!

### Meetings

Note: On Thursday 27.01 we will be in KJL2 in Kjelhuset and on Friday 28.01 in S8 in Sentralbygget.

- Thursdays 10.15-12.00, on Zoom or in room K26 in Kjemiblokk 4. Zoom link for Thursday is here
- Fridays 08.30-10.00, on Zoom or in room R93 in Realfagbygget. Zoom link for Friday is here

Remember that we start 08:30 on Fridays and not 08:15, and that we have no breaks.

The first meeting is Thursday, January 13th, and the last meeting is Friday, May 6th.

### Lecturer

- Sondre Kvamme
- 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 Øyving 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 (particularly in an online setting) 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
- For Zoom meetings, if you have an ipad or tablet, try to familiarise yourself with how to use it in conjunction with Zoom to write and present mathematics. This will make discussions in class much easier.
- For Zoom meetings, leave your video on during class if possible (the meetings will not be recorded).
- For Zoom meetings, make sure your name appears correctly.

### 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

### Reference Group

The reference group is:

If you have any comments, concerns or feedback to the course please share them with me or the reference group.

First reference group meeting: 25/01

Second reference group meeting: 09/03

**First meeting**: People seem to be in general happy with the course. The amount of exercises seem to be good, but it would be useful if all necessary definition are given in the exercises (i.e. local ring, connectedness of rings etc…). Also, would be useful with references to where the material from the lectures can be found in the literature.