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401-2003-00L 7 Credits BSC D-PHYS , D-MATH
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Algebra I

Lecturers & Examiners: Prof. Dr. Lorenz Halbeisen
The two-semester course Algebra I / Algebra II is offered for the last time in its current version in the Autumn Semester 2021 / Spring Semester 2022.
VVZ CR n/a

Last Updated: 2026-02-05 15:47:57

Abstract

Introduction and development of some basic algebraic structures - groups, rings, fields.

Objective

Introduction to basic notions and results of group, ring and field theory.

Content

Group Theory: basic notions and examples of groups, subgroups, factor groups, homomorphisms, group actions, Sylow theorems, applications Ring Theory: basic notions and examples of rings, ring homomorphisms, ideals, factor rings, euclidean rings, principal ideal domains, factorial rings, applications Field Theory: basic notions and examples of fields, field extensions, algebraic extensions, applications

Resources

Literature

Karpfinger-Meyberg: Algebra, Spektrum Verlag S. Bosch: Algebra, Springer Verlag B.L. van der Waerden: Algebra I und II, Springer Verlag S. Lang, Algebra, Springer Verlag A. Knapp: Basic Algebra, Springer Verlag J. Rotman, "Advanced modern algebra, 3rd edition, part 1" http://bookstore.ams.org/gsm-165/ J.F. Humphreys: A Course in Group Theory (Oxford University Press) G. Smith and O. Tabachnikova: Topics in Group Theory (Springer-Verlag) M. Artin: Algebra (Birkhaeuser Verlag) R. Lidl and H. Niederreiter: Introduction to Finite Fields and their Applications (Cambridge University Press)

Learning Materials (Links)

General Information

Language
German
Levels
BSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 20 minutes
Für den Semesterkurs Algebra I gibt es keine Leistungselemente, die in einen Notenbonus umgerechnet werden.(Für den Jahreskurs ist eine MC-Zwischenprüfung vorgesehen.)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.

Course Components

Type Title Time & Place Hours
lecture Algebra I
  • Wed 14:15-16:00 (HG G 5)
  • Fri 08:15-10:00 (HG G 5)
4 h weekly
exercise Algebra I
Groups are selected in myStudies.
  • Wed 16:15-18:00 (HG D 5.2)
  • Wed 16:15-18:00 (HG E 33.3)
  • Wed 16:15-18:00 (HG F 26.5)
  • Wed 16:15-18:00 (HG G 26.5)
  • Wed 16:15-18:00 (LFW C 1)
2 h weekly

Offered In