Introduction to algebraic number theory

3-4 hours of lectures per week.

Lecturer: Steffen Bentzen

Content:
Aims and objectives:

• To acquire a basic understanding of algebraic number fields, in particular quadratic and cyclotomic fields.

Keywords:

• Ring of integers, ideals, Galois theory, decomposition laws.

Course description: An algebraic number is a root of a rational polynomial, and an algebraic number field is a field obtained from Q by adjoining an algebraic number. In this course we study the basic theory of such fields. An essential property of the ordinary integers is the unique factorization theorem. This theorem is no longer valid for a general number field. A major theme in the course will be to "repair" this defect.

The students are required to participate actively in the course, in the form of either seminars or exercises (depending on the number of participants).

Prerequisites: 1. del plus a general algebraic interest.

Literature: Notes.