### 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 1.029 Kollegiengebäude Mathematik (20.30) | ||

Email: herrlich@kit.edu | ||

Problem classes | Sven Caspart | |

Office hours: by appointment | ||

Room 1.035 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**.