Course detail
Groups and Rings
FSI-SG0Acad. year: 2024/2025
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
Department
Entry knowledge
Linear algebra, general algebra
Rules for evaluation and completion of the course
Course credit: the attendance, satisfactory solutions of homeworks
Lectures: recommended
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.
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
G. Bini and F. Flamini, Finite Commutative Rings and Their Applications, Springer 2002
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
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
Recommended reading
Not applicable.
Elearning
eLearning: currently opened course
Classification of course in study plans
Type of course unit
Lecture
26 hod., optionally
Teacher / Lecturer
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
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
Elearning
eLearning: currently opened course