406-2004-AAL  Algebra II

SemesterHerbstsemester 2019
DozierendeR. Pandharipande
Periodizitätjedes Semester wiederkehrende Veranstaltung
LehrspracheEnglisch
KommentarBelegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben.

Alle anderen Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen.


KurzbeschreibungGalois theory and related topics.

The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
LernzielIntroduction to fundamentals of field extensions, Galois theory, and related topics.
InhaltThe 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.
LiteraturJoseph 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.
Voraussetzungen / BesonderesAlgebra I, in Rotman's book this corresponds to the topics treated in the Chapters A3 and A4.