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406-2004-AAL 6 Credits MSC D-MATH
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Algebra II

Lecturers & Examiners: Prof. Dr. Lorenz Halbeisen
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
VVZ CR n/a

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
The content coincides with the content of the course unit 401-2004-00L Algebra II and changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.

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