Course Syllabus for

Group and Ring Theory
Grupp- och ringteori

MATP33F, 7.5 credits

Valid from: Spring 2021
Decided by: Professor Thomas Johansson
Date of establishment: 2020-09-24

General Information

Division: Mathematics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: MATP33
Teaching language: English


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.


Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must

Judgement and Approach

For a passing grade the doctoral student must 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.

Course Contents

• 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.

Course Literature

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

Instruction Details

Types of instruction: Lectures, seminars

Examination Details

Examination formats: Written exam, oral exam
Grading scale: Failed, pass

Admission Details

Assumed prior knowledge: FMAN10 Algebraic structures

Course Occasion Information

Contact and Other Information

Course coordinators:

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