## Generalities

Organizer: Lars Kindler

Date: Tuesdays, 4-6pm, Place: SR 140/A7, Arnimallee 7

**Official website in course registry**
Please send questions and comments to kindler - at - math.fu-berlin.de

or come to office 109, Arnimallee 3

**Prerequisites:** Linear Algebra and some familiarity with basic notions of algebra like groups, rings, fields, ideals, normal subgroups, etc.

**Guidelines:** This is a seminar, which means

*the participants* give the talks. Please write to me if you would like to reserve one of the talks for you, or if you have any questions.

**First meeting:** Tuesday, April 18

## Description

Algebraic numbers are complex numbers which are zeroes of a
polynomial with rational coefficients. For example $\sqrt{2},
2^{1/3}$, $i$ or $e^{\frac{2\pi i}{n}}$. In this seminar we
want to study algebraic numbers in the context of modern
algebra. The notion of an algebraic extension of fields is
central. Galois theory describes all (separable) algebraic
extensions of a given field using the language of group theory. We will
first discuss the Galois theory for finite algebraic
extensions. It depends on the prior knowledge of the
participants of the seminar how extensive this first stage will be.
We will then study several applications and generalizations.

You can find a comprehensive program

here.