*Instructor:* Dr. András BÍRÓ

*Text: *Chapters 1 and 2 of J. Neukirch: Algebraic Number Theory, Springer,
1999

*Reference book: *J. Neukirch: Algebraic Number Theory, Springer,
1999

*Prerequisite:* elementary number theory, basic theorems of linear algebra,
basic notions of abstract algebra (fields, rings, modules)

*Course description:*the aim of the course is to present the basic properties
of algebraic number fields (i.e finite extensions of the field of rational
numbers)

*Topics:*

integral closure of a subring, existence of an integral basis

Dedekind domains, unique factorization of prime ideals

Dedekind domains, unique factorization of prime ideals

structure of the units of an algebraic number field: Dirichlet`s Unit Theorem

decomposition of a prime ideal in an extension

cyclotomic fields

p-adic numbers, local fields