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401-2004-00L 6 Credits BSC D-PHYS , D-MATH
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Algebra II

Lecturers: Prof. em. Dr. Richard Pink
Examiners: Prof. em. Dr. Richard Pink, Prof. Dr. Lorenz Halbeisen
VVZ CR n/a

Last Updated: 2026-02-05 16:22:24

Abstract

Selected topics concerning rings, groups, fields, including Galois theory.

Objective

Selected topics concerning rings, groups, fields, including Galois theory.

Content

Ring theory: elementary divisor theorem, classification of finitely generated modules over principal ideal domains, applications to finitely generated abelian groups and the Jordan normal form. Structure theory of groups: finite groups, composition series, solvable groups, semidirect products, p-groups, Sylow theorems. Structure of field extensions: algebraic closure, separable polynomials, finite fields, separable and/or normal field extensions, Galois extensions, Galois correspondence, symmetric functions, cyclotomic fields, abelian field extensions, solvable field extensions, theorem of Abel-Ruffini.

Resources

Literature

Bosch: Algebra. Springer Verlag. Fischer: Lehrbuch der Algebra. Vieweg Verlag. Lang: Algebra. Springer Verlag. Jantzen, Schwermer: Algebra. Springer Verlag. Rotman: Advanced Modern Algebra

Learning Materials (Links)

General Information

Language
German
Levels
BSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 120 minutes, oral 20 minutes
Aids
keine
Betrifft den Jahreskurs Algebra I und II: ab Sommer 2023 wird die Prüfung als Jahreskurs für allfällige Nachzügler aus den beiden Teilprüfungen Algebra I und Algebra II bestehen, welche in der betreffenden Prüfungssession auch als Prüfungen für die Semesterkurse stattfinden.Die in den Semesterkursen angebotenen Lernelemente gelten auch für den Jahreskurs.

Course Components

Type Title Time & Place Hours
lecture Algebra II
  • Mon 13:15-14:00 (HG F 3)
  • Wed 14:15-16:00 (HG F 3)
3 h weekly
exercise Algebra II
Groups are selected in myStudies.
  • Tue 16:15-18:00 (CHN D 44)
  • Tue 16:15-18:00 (ETZ E 7)
  • Tue 16:15-18:00 (HG E 33.5)
  • Tue 16:15-18:00 (HG G 26.3)
  • Tue 16:15-18:00 (NO D 11)
2 h weekly

Offered In