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Algebra II
Last Updated: 2026-06-01 11:33:48
Abstract
Galois theory and related topics.The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
Objective
Introduction to fundamentals of field extensions, Galois theory, and related topics.
Content
The main topic is Galois Theory. Starting point is the problem of solvability of algebraic equations by radicals. Galois theory solves this problem by making a connection between field extensions and group theory. Galois theory will enable us to prove the theorem of Abel-Ruffini, that there are polynomials of degree 5 that are not solvable by radicals, as well as Galois' theorem characterizing those polynomials which are solvable by radicals.
Resources
Literature
Joseph J. Rotman, "Advanced Modern Algebra" third edition, part 1, Graduate Studies in Mathematics,Volume 165 American Mathematical Society Galois Theory is the topic treated in Chapter A5.
General Information
- Language
- English
- Levels
- MSC
- Frequency
- Semesterly recurring
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| revision course / private study |
Algebra II
Self-study course. No presence required.
|
No time listed | 180 h semesterly |
Offered In
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Auflagen-Lerneinheiten (Das untenstehende Lehrangebot gilt nur für MSc Studierende mit Zulassungsauflagen.)
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