Algebra (englisch) (Winter Semester 2014/15)
- Lecturer: Prof. Dr. Frank Herrlich
- Classes: Lecture (0102200), Problem class (0102300)
- Weekly hours: 4+2
The course will give an introduction to basic concepts in field threory and ring theory.
The lectures will be in English.
In the first week, the lecture takes place on Wednesday and Thursday (9.45 to 11.15). The first problem class is on Friday, October 24, from 11.30 to 13.00.
In the week before Christmas the lecture and the tutorial will be swapped. The lecture will take place on Tuesday, 16.12.2014, 17:30 in the room 1C-03 (Allianzgebäude) and the tutorial will take place on Wednesday, 17.12.2014, 9:45 in the lecture hall AOC 201 (chemistry building).
There will be no tutorial at 23 December 2014.
| Schedule | |||
|---|---|---|---|
| Lecture: | Wednesday 9:45-11:15 | AOC 201 | Begin: 22.10.2014, End: 13.2.2015 |
| Friday 11:30-13:00 | Neuer Hörsaal | ||
| Problem class: | Thursday 9:45-11:15 | Chemie-Hörsaal II | Begin: 24.10.2014 |
| Lecturers | ||
|---|---|---|
| Lecturer | Prof. Dr. Frank Herrlich | |
| Office hours: By appointment (per e-mail) | ||
| Room 1.022 Kollegiengebäude Mathematik (20.30) | ||
| Email: herrlich@kit.edu | Problem classes | Sven Caspart |
| Office hours: by appointment | ||
| Room Kollegiengebäude Mathematik (20.30) | ||
| Email: sven.caspart@kit.edu | ||
Contents
1. Field theory
Algebraic field extensions, separability, normal extensions, Galois theory.
Roots of unity, cyclotomic fields, solution of polynomial equations by radicals, solvable groups.
2. Valuation theory
Valuations, absolute values and norms on rings.
p-adic numbers, nonarchimedean valuations.
Discrete valuation rings, extension of valuations.
3. Ring theory
Modules over rings, tensor product of modules, multilinear algebra.
Noetherian rings, ring of polynomials, Hilbert's basis theorem.
Integral ring extensions, integral closure; normalization, Dedekind domains.
Exercise Sheets
The exercise sheets can be found in the Ilias course.
Examination
The oral exams will take place on 2 March, 16 March and 30 March 2015. Students who want to take the exam should sign in to the time table which can be found in the secretary's office (room 4A-21.1, Allianz building). Possible times are listed in the table there.
In addition you must register the exam in the Campus Management for Students.