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, Dedekind domains and DVRs, Noether Normalization Lemma, Completion of a ring, Dimension theory and Hilbert polynomials.
Course info
- Lectures: TTh 1:00-2:15
- Classroom: LOM 205
- 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 5-6pm
Homework Sets
Schedule
| Week | Dates | Topics |
|---|---|---|
| 1 | 14 Jan - 20 Jan | Simple, Semi-simple rings, Jacobson Radical |
| 2 | 21 Jan - 27 Jan | Jacobson Radical cont. |
| 3 | 28 Jan - 3 Feb | Maschke's theorem |
| 4 | 4 Feb - 10 Feb | Representation theory |
| 5 | 11 Feb - 17 Feb | Primary Decomposition |
| 6 | 18 Feb - 24 Feb | Krull Intersection Theorem, Integral Extensions |
| 8 | 4 March - 10 March | Going-up, going-down lemmas |
| 9 | 24 March - 31 March | Noether Normalization |
| 10 | 1 April - 8 April | Dimension theory - Hilbert functions (polynomial ring case) |
| 11 | 9 April - 14 April | Dimension theory - equivalent definitions of dimension |
| 12 | 15 April - 21 April | Completions |
| 13 | 22 April - 29 April | Review |