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HU Credits:
3
Degree/Cycle:
2nd degree (Master)
Responsible Department:
Mathematics
Semester:
1st Semester
Teaching Languages:
English
Campus:
E. Safra
Course/Module Coordinator:
Borys Kadets
Coordinator Office Hours:
By appointment
Teaching Staff:
Dr. Borys Kadets
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:
Marcus "Number Fields"
Grading Scheme :
Essay / Project / Final Assignment / Home Exam / Referat 20 %
Submission assignments during the semester: Exercises / Essays / Audits / Reports / Forum / Simulation / others 80 %
Additional information:
The course will be given in English
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