406-2004-AAL Algebra II
| Semester | Herbstsemester 2020 |
| Dozierende | R. Pink |
| Periodizität | jedes Semester wiederkehrende Veranstaltung |
| Lehrsprache | Englisch |
| Kommentar | Belegung 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. |
| Kurzbeschreibung | Galois theory and related topics. The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. |
| Lernziel | Introduction to fundamentals of field extensions, Galois theory, and related topics. |
| Inhalt | 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. |
| Literatur | 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. |
| Voraussetzungen / Besonderes | Algebra I, in Rotman's book this corresponds to the topics treated in the Chapters A3 and A4. |