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Algebraic number theory 2

Code: 92920
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Marko Tadić - Lectures
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 45
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES: The aim of the course is to present the fundamental results of the algebraic number theory, and to illustrate applications of these results to the last Fermat theorem.

COURSE DESCRIPTION AND SYLLABUS:
1. Traces and norms in field extensions.
2. Discriminant of n-tuple.
3. Computation of discriminant in some cases.
4. Structure of the additive group of the ring of integers in the algebraic number fields.
5. Integral bases
6. Discriminant of an algebraic number field.
7. Ring of integers in the cyclotomic fields, the case of prime power.
8. Ring of integers in the cyclotomic fields, general case.
9. Dedekind's domains and the rings of integers in algebraic number fields.
10. Ideal class group.
11. Factorization in Dedekind'sw domains.
12. Factorization of ideals in extensions of algebraic number fields, examples.
13. Ramification index, inertial degree.
14. The sums of four squares.
Literature:
  1. D. A. Marcus: Number fields
  2. P. Samuel: Algebraic Theory of Numbers
  3. J. - P. Serre: A Course in Arithmetic
Prerequisit for:
Enrollment :
Passed : Algebraic number theory 1
4. semester
Mandatory course - Regular study - Theoretical Mathematics
Consultations schedule: