HU Credits: 3

Degree/Cycle: 2nd degree (Master)

Responsible Department: Mathematics

Semester: 1st Semester

Teaching Languages: Hebrew

Campus: E. Safra

Course/Module Coordinator: Shaul Zemel

Coordinator Email: shaul.zemel@mail.huji.ac.il

Coordinator Office Hours: By appointment

Teaching Staff:
Dr. Shaul Zemel

Course/Module description:
Introduction to the basic properties of algebraic numbers.

Course/Module aims:
Getting acquainted with the basic properties of the rings of integers in number fields, decomposition of prime ideals in extensions, finiteness of the class number, finite generation of the group of units, p-adic numbers, Hensel's lemma.

Learning outcomes - On successful completion of this module, students should be able to:
- to compute rings of integers in algebraic number fields of low degree
- to decompose an ideal to a product of primes
- to evaluate the ramification indices and inertial degrees of primes in extensions of low degree
- to compute units of number fields
- to prove simple properties of algebraic number fields.

Attendance requirements(%):

Teaching arrangement and method of instruction: Lecture

Course/Module Content:
Traces and norms, discriminants, integral ring extensions, number fields, integer rings, Dedekind rings, ramification and inertia, cyclotomic fields, the geometric embedding, finiteness of the class group, the structure of the group of units, the p-adic fields, Hensel's lemma.

Required Reading:
None

Additional Reading Material:
Lecture notes will be published as we advance with the course

Grading Scheme :
Essay / Project / Final Assignment / Home Exam / Referat 100 %

Additional information:
In case non-Hebrew speaking students are present, the course will be given in English