1. komponenta

Lecture type	Total
Lectures	30
Exercises	30

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: The goal of the course is to introduce the most important notions and to learn fundamental results of the group theory, rings, modules, fields and generally algebras. Especially in course will be described a connections between main objectives mentioned above with another important math theory like number theory and representation theory.

COURSE DESCRIPTION AND SYLLABUS:
First section: Group theory (7 weeks)
1. Definition of the semigroup, group, subgroup
2. Normal subgroup and quotient group
3. Examples of the groups (cyclic groups, symmetric group, dihedral group, etc.)
4. Homomorphisms of the groups
5. Direct products and sums of the groups
6. The p-groups and the Sylow theorems
Second section: Ring, Fields and Algebras (6 weeks)
1. Definition of the rings, subrings and ideals
2. Homomorphisms of the rings
3. Factorizations in commutative rings and principal ideal domain
4. Rings of polynomials and the other important examples
5. Definition of the fields, subfield and the field extensions
6. Simple and finitely extensions
7. Finite fields
8. Examples of algebras (associative and nonassociative)
Third section: Modules (2 weeks)
Definition of the modules, submodules and quotient modules
1. The main theorems and examples of simple (semisimple) modules

Enrollment :
Passed : Linear algebra 2

Algebra - Regular study - Mathematics Education

Algebra - Regular study - Mathematics Education