Course detail

Groups and Rings

FSI-SG0Acad. year: 2023/2024

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.

Language of instruction

Czech

Number of ECTS credits

2

Mode of study

Not applicable.

Guarantor

doc. RNDr. Miroslav Kureš, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Linear algebra, general algebra

Rules for evaluation and completion of the course

Course credit: the attendance, satisfactory solutions of homeworks
Lectures: recommended

Aims

Students will be made familiar with advanced algebra, in particular group theory and ring theory.
The course makes access to mastering in a wide range of results of algebra.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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

Recommended reading

Not applicable.

Classification of course in study plans

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

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

doc. RNDr. Miroslav Kureš, Ph.D.

Syllabus

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