The Hebrew University Logo
close window close
PDF version
Last update 20-08-2021
HU Credits: 3

Degree/Cycle: 2nd degree (Master)

Responsible Department: Mathematics

Semester: 1st Semester

Teaching Languages: English and Hebrew

Campus: E. Safra

Course/Module Coordinator: Ari Shnidman

Coordinator Email:

Coordinator Office Hours: By appointment

Teaching Staff:
Dr. Schneidman Ari

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, p-adic numbers, Hensel's lemma, finiteness of the class number, finite generation of the group of units.

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, p-adic fields, Hensel's lemma, finiteness of the class group, the structure of the group of units.

Required Reading:

Additional Reading Material:

Course/Module evaluation:
End of year written/oral examination 0 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 100 %
Assignments 0 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %

Additional information:
Students needing academic accommodations based on a disability should contact the Center for Diagnosis and Support of Students with Learning Disabilities, or the Office for Students with Disabilities, as early as possible, to discuss and coordinate accommodations, based on relevant documentation.
For further information, please visit the site of the Dean of Students Office.