1. komponenta

Lecture type	Total
Lectures	45

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

COURSE AIMS AND OBJECTIVES: This course is the final, second part of the standard advanced course in algebra. Basic structures that are studied in the course are rings, modules and fields.

COURSE DESCRIPTION AND SYLLABUS:
1. Rings of quotients.
2. Polynomial rings.
3. Zeros of polynomials, derivatives, Gauss lemma.
4. Factorization in polynomial rings.
5. Factoriality of the polynomial rings. Eisenstein's criterion.
6. Modules. Basic definitions.
7. Sums and products of modules, exact sequences.
8. Functor Hom.
9. Free modules and vector spaces.
10. Tensor products of modules.
11. Algebraic and transcendent extensions.
12. Fundamental theorem of the Galois theory.
13. Splitting fields, algebraic closure.

1. Algebra, T. W. Hungerford, Springer Verlag, 1996.
2. Algebra, S. Lang, Addison-Wesley, 1984.

Enrollment :
Attended : Algebra 1

Examination :
Passed : Algebra 1

Mandatory course - Regular study - Theoretical Mathematics