Algebra II
Instructors: Dr. Moritz RahnShortname: 08.105.160
Course No.: 08.105.160
Course Type: Vorlesung/Übung
Requirements / organisational issues
The lecture course "Algebra II" is (not completely surprising) designed as a continuation of the course "Algebra I". We assume some background in basic ring theory and field theory. In contrast to this, the theory of non-abelian groups will most likely only play a minor role (if at all). Moreover, we do NOT assume that the student knows about modules.Recommended reading list
TBAContents
This lecture course is an introduction to commutative algebra and homological algebra. For us, this means that we study (often commutative) rings and modules over such rings. Modules over rings generalize simultaneously vector spaces (modules over fields) and abelian groups (modules over the integers). Central topics are localization theory of commutative rings (generalizing quotient fields of integral domains), integral ring extensions (generalizing algebraic field extensions) and Noetherian rings (generalizing principal ideal domains). We will study tensor products and homomorphism groups of modules together with their exactness properties. This leads most naturally to torsion products and extension groups and thereby into the realm of homological algebra.The basic techniques of homological algebra play a central role in moden algebraic geometry, algebraic topology and representation theory, and this lecture course hence provides a preparation for these more advanced topics.
Dates
| Date (Day of the week) | Time | Location |
|---|---|---|
| 04/17/2018 (Tuesday) | 10:00 - 12:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 04/19/2018 (Thursday) | 14:00 - 16:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 04/24/2018 (Tuesday) | 10:00 - 12:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 04/26/2018 (Thursday) | 14:00 - 16:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 05/03/2018 (Thursday) | 14:00 - 16:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 05/08/2018 (Tuesday) | 10:00 - 12:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 05/15/2018 (Tuesday) | 10:00 - 12:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 05/17/2018 (Thursday) | 14:00 - 16:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 05/22/2018 (Tuesday) | 10:00 - 12:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 05/24/2018 (Thursday) | 14:00 - 16:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 05/29/2018 (Tuesday) | 10:00 - 12:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 06/05/2018 (Tuesday) | 10:00 - 12:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 06/07/2018 (Thursday) | 14:00 - 16:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 06/12/2018 (Tuesday) | 10:00 - 12:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 06/14/2018 (Thursday) | 14:00 - 16:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 06/19/2018 (Tuesday) | 10:00 - 12:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 06/21/2018 (Thursday) | 14:00 - 16:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 06/26/2018 (Tuesday) | 10:00 - 12:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 06/28/2018 (Thursday) | 14:00 - 16:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 07/03/2018 (Tuesday) | 10:00 - 12:00 | 04 516 2413 - Neubau Physik/Mathematik |
| 07/05/2018 (Thursday) | 14:00 - 16:00 | 04 516 2413 - Neubau Physik/Mathematik |