Spezialvorlesung: Algebraische Zahlentheorie
- LVA-Leiter:
- Ao.Prof. Dipl.-Ing. Dr.techn. Günter Lettl
- Koordination der LVA:
- If you are interested in this
lecture (or at least its introductory start), please tick the
dates which are suited for you in DOODLE.
You will find the dates and details for the lectures (up to Nov 4) on this page soon.
Description
When dealing with Diophantine Equations or other number theoretic problems, one is often led to investigate arithmetical questions (units, factorization into irreducibles, ... ) in subrings of finite dimensional extension fields of the rationals, socalled "algebraic number fields". The arithmetic of such rings (more generally, of Dedekind rings) is well understood, and is the central theme of this lecture.
Contents of the course
- Algebraic number fields and algebraic integers,
- fractional ideals and class group,
- structure of the unit group,
- decomposition of prime ideals under field extension,
- eventually: discrete valuations and localizations.
Remarks on computational methods and algorithms for doing arithmetic in algebraic number fields are also presented.
Prerequisites
Commutative algebra and field extensions;
other algebraic prerequisites will be explained during the lecture (if there is need for)
Language
Englisch (if requested by at least one participant); otherwise German.
Audience
Master- and PhD students.