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Algebraic structures

Code: 45774
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Filip Najman - Lectures
prof. dr. sc. Boris Širola - Lectures
Lecturers: dr. sc. Ana Kontrec - Exercises
prof. dr. sc. Boris Širola - Exercises
English level:

1,0,0

All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.
Load:

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 30
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
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
Literature:
1. semester
Algebra i osnove matematike - Mandatory studij - Mathematics and Computer Science Education

2. semester
Algebra i osnove matematike - Mandatory studij - Mathematics and Computer Science Education
Consultations schedule: