The topics presented in the course will include: * Basics facts about rings, ideals, and modules * Constructions of rings: quotients, polynomial rings, localization * The prime spectrum of a ring * Chain conditions, Noetherian/Artinian rings and modules * The tensor product of modules over commutative rings * Some homological algebra * Integral extensions, going up, going down * Finitely generated algebras over fields, including the Noether Normalization Theorem and the Nullstellensatz * Discrete valuation rings and some applications * Dimension theory
Algebra I/II (or a similar introduction to the basic concepts of ring theory, including field theory).
The exam is a 30 minute oral exam. The first question on your exam will be chosen randomly from this collection of questions.
The new exercises will be posted here on Fridays, and are due in Dmitrii Krekov's box in HG J 68 the next Friday at 12:00.
| exercise sheet | due by | solutions |
|---|---|---|
| Exercise sheet 1 | September 29 | Solutions 1 |
| Exercise sheet 2 | October 6 | Solutions 2 |
| Exercise sheet 3 | October 13 | Solutions 3 |
| Exercise sheet 4 | October 20 | Solutions 4 |
| Exercise sheet 5 | October 27 | Solutions 5 |
| Exercise sheet 6 | November 3 | Solutions 6 |
| Exercise sheet 7 | November 10 | Solutions 7 |
| Exercise sheet 8 | November 17 | Solutions 8 |
| Exercise sheet 9 | November 24 | Solutions 9 |
| Exercise sheet 10 | December 1 | Solutions 10 |
| Exercise sheet 11 | December 8 | Solutions 11 |
| Work on the exam questions | N/A | No solutions, obviously |
| Some practice problems | N/A |
The first exercise classes will be on 28 Sept.
| time | room | assistant | language |
|---|---|---|---|
| Th 09-10 | HG E 1.2 | Dmitrii Krekov/Semyon Abramyan | English |
| Th 12-13 | HG E 1.2 | Dmitrii Krekov/Semyon Abramyan | English |