MATP33F

Temporary

Group and Ring Theory

7.5

Course given jointly for second and third cycle

7151 (Centre of Mathematical Sciences / Mathematics)

2020-09-24

Professor Thomas Johansson

English

Every other spring semester

The course aims to provide, in comparison with the course Algebraic structures, a deeper understanding of group theory and ring theory as a basis for further studies in algebraic subject areas, and to provide general mathematical knowledge.

• Groups: Permutation groups. Burnside's lemma with application to Pólya arithmetic. Sylow's theorems. Symmetric and alternating groups. The structure of finitely generated Abelian groups.
• Rings: Noetherian and Artinian rings and modules. Artin-Wedderburn's theorem. Finitely generated modules over a principal ideal domain with application to Jordan's normal form of matrices.
• Linear algebra: Multilinear mappings. Tensor products.

be able to, in detail, explain the concepts, theorems and methods included in the course,

be able to identify the most important theorems in the course and present their proofs.

in connection with problem solving be able to demonstrate the ability to integrate knowledge from the different parts of the course,

be able to independently identify problems that can be solved by methods that are part of the course and use appropriate solution methods,

be able to explain the solution to a mathematical problem within the course framework, in speech and in writing, logically coherently and with adequate terminology.

be able to argue for the importance of group theory and ring theory as tools in other areas such as algebraic geometry and algebraic number theory, and discuss their limitations.

Lectures

Seminars

Written exam

Oral exam

Failed, pass

FMAN10 Algebraic structures

Bhattacharya, P. B., Jain, S. K. & Nagpaul, S. R.: Basic Abstract Algebra. Cambridge University Press, 1994. ISBN 9780521466295.

MATP33F

2020-09-24

Professor Thomas Johansson