Course detail

Groups and Rings

FSI-SG0Acad. year: 2020/2021

In the course Groups and rings, students are familiarised with selected topics of algebra. The acquired knowledge is a starting point not only for further study of algebra and other mathematical disciplines, but also a necessary assumption for a use of algebraic methods in a practical solving of number of problems.

Learning outcomes of the course unit

The course makes access to mastering in a wide range of results of algebra.


Linear algebra, general algebra


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

M.F. Atiyah and I.G. Macdonald, Introduction To Commutative Algebra, Addison-Wesley series in mathematics, Verlag Sarat Book House, 1996
O. Bogopolski, Introduction to Group Theory, European Mathematical Society 2008
G. Bini and F. Flamini, Finite Commutative Rings and Their Applications, Springer 2002

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline.

Assesment methods and criteria linked to learning outcomes

Course credit: the attendance, satisfactory solutions of homeworks

Language of instruction


Work placements

Not applicable.


Students will be made familiar with advanced algebra, in particular group theory and ring theory.

Specification of controlled education, way of implementation and compensation for absences

Lectures: recommended

Classification of course in study plans

  • Programme B-MAI-P Bachelor's, 2. year of study, winter semester, 2 credits, elective
  • Programme B-FIN-P Bachelor's, 2. year of study, winter semester, 2 credits, elective

Type of course unit



26 hours, optionally

Teacher / Lecturer


1. Groups, subgroups, factor groups
2. Group homomorphisms, group actions on a set, group products
3. Topological, Lie and algebraic groups
4. Jets of mappings, jet groups
5. Rings and ideals
6. Euclidean rings, PID and UFD
7. Monoid a group rings
8. Gradede rings, R-algebras
9. Polynomials and polynomial morphisms
10. Modules and representations
11. Finite group and rings
12. Quaternionic algebras
13. Reserve - the topic to be specified