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406-2005-AAL 12 Credits MSC D-MATH
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Algebra I and 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: 2026-02-05 16:02:15

Abstract

Introduction and development of some basic algebraic structures - groups, rings, fields including Galois theory, representations of finite groups, algebras.The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.

Content

Basic notions and examples of groups; Subgroups, Quotient groups and Homomorphisms, Group actions and applications Basic notions and examples of rings; Ring Homomorphisms, ideals, and quotient rings, rings of fractions Euclidean domains, Principal ideal domains, Unique factorization domains Basic notions and examples of fields; Field extensions, Algebraic extensions, Classical straight edge and compass constructions Fundamentals of Galois theory Representation theory of finite groups and algebras

Resources

Literature

Joseph J. Rotman, "Advanced Modern Algebra" third edition, part 1, Graduate Studies in Mathematics,Volume 165 American Mathematical Society

General Information

Language
English
Levels
MSC
Frequency
Semesterly recurring

Examination

Type
session examination
Mode
oral 30 minutes
The content coincides with the content of the course units 401-2003-00L Algebra I and 401-2004-00L Algebra II and changes with the examiners. Candidates must therefore contact the examiner in person before studying the material.Students who take the oral examination in the examination session Winter JAHR were allowed to take part in the learning tasks that were offered for the two-semester course in the Autumn Semester 2020 and Spring Semester JAHR.

Course Components

Type Title Time & Place Hours
revision course / private study Algebra I and II
Self-study course. No presence required.
No time listed 360 h semesterly

Offered In