406-2005-AAL Algebra I and II
| Semester | Autumn Semester 2018 |
| Lecturers | M. Burger, E. Kowalski |
| Periodicity | every semester recurring course |
| Language of instruction | English |
| Comment | 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. |
| 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. |
| Learning objective | |
| 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 |
| Lecture notes | For a summary of the content and exercises with solutions of my lecture courses in HS2015 and FS2016 see: Link https://www2.math.ethz.ch/education/bachelor/lectures/fs2016/math/algebra2/ |
| Literature | S. 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 |