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406-2005-AAL  Algebra I and II

SemesterSpring Semester 2017
LecturersL. Halbeisen
Periodicityevery semester recurring course
Language of instructionEnglish
CommentEnrolment 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.


AbstractIntroduction 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.
Objective
ContentBasic 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
LiteratureS. Lang, Algebra, Springer Verlag
B.L. van der Waerden: Algebra I und II, Springer Verlag
I.R. Shafarevich, Basic notions of algebra, Springer verlag
G. Mislin: Algebra I, vdf Hochschulverlag
U. Stammbach: Algebra, in der Polybuchhandlung erhältlich
I. Stewart: Galois Theory, Chapman Hall (2008)
G. Wüstholz, Algebra, vieweg-Verlag, 2004
J-P. Serre, Linear representations of finite groups, Springer Verlag