Modern Algebra II
We would cover as many of the following topics as we have time for.
- Non-commutative rings: Jacobson Radical, Wedderburn-Artin Theorem, Modules over group algebras, irreducible representations, Maschke's theorem.
- Commutative rings: Primary decomposition of modules, Lasker-Noether Theorem, Krull Intersection theorem, Krull dimension, Integral extensions, Going Up/Going Down Theorems, Noether Normalization Lemma, Completion of a ring, Dimension theory and Hilbert polynomials.
Course info
- Lectures: TTh 11:35 am-12:50 pm
- Classroom: LOM 215
- Office: DL 406
Syllabus
You can find the syllabus here.Office hours
If you need help with the course or you have questions regarding the material or the homeworks or you would just want to pick up your homework, please don't hesitate to stop by my office or write me an email. If the time is inconvenient you can arrange an appointment.Office hours: Monday 4-5pm
Homework Sets
- Homework Set 1 due Feb 20.
- Homework Set 2 due March 5.
- Homework Set 3 due March 23.
- Homework Set 4 due April 14.
- Homework Set 5 presentation in class.
Schedule
| Week | Dates | Topics |
|---|---|---|
| 1 | 13 Jan - 19 Jan | Simple, Semi-simple rings, Jacobson Radical |
| 2 | 20 Jan - 26 Jan | Jacobson Radical cont. |
| 3 | 27 Jan - 4 Feb | Wedderburn-Artin Theorem |
| 4 | 4 Feb - 9 Feb | Maschke's theorem |
| 5 | 10 Feb - 16 Feb | Representation theory, Characters |
| 6 | 17 Feb - 23 Feb | Character Tables, Burside Theorems |
| 7 | 24 Feb - 1 March | Primary Decomposition |
| 8 | 2 March - 6 March | Primary Decomposition |
| 9 | 23 March - 29 March | Krull Intersection Theorem, Artin-Rees lemma, Integral Extensions |
| 10 | 30 March - 5 April | Cohen-Seidenberg Theory |
| 11 | 6 April - 12 April | Noether Normalization, Dimension theory - 1 |
| 12 | 13 April - 19 April | Dimension theory - 2 |
| 13 | 20 April - 24 April | Dimension theory - 3, Completions |