401-2003-00L  Algebra I

SemesterAutumn Semester 2019
LecturersR. Pink
Periodicityyearly recurring course
Language of instructionGerman


AbstractIntroduction and development of some basic algebraic structures - groups, rings, fields.
Learning objectiveIntroduction to basic notions and results of group, ring and field
theory.
ContentGroup 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
LiteratureKarpfinger-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)