After successful completion of the course, students are able to 

• explain the ideal-structure of algebraic integral rings and to deduce their main properties,

• define algebraic number fields and to formulate applications,

• apply Galois theory to algebraic number fields,

• explain the concept of Dedekind domains and to deduce their mein properties

• formulate and apply the Dirichlet unit theorem and to sketch its proof,

• explain the class number of algebraic number fields and to calculate it for quadratic number fields and
  

• to sketch the ideas and methods that are needed to proof the main theorems.

basic concepts of algebraic number theory, in particular with the ideal structure of integral rings of algebraic number fields.

Algebraic number fields, Galois theory, Dedekind rings, Dirichlet's unit theorem, class number

Blackboard lecture

Die Vorlesung findet (ab dem Fr., 8.3.)

   Mi, 14:00-15:00
   Fr, 12:00-13:30

im Sem.R. DB gelb 05 B statt.

KEINE Vorlesungen sind am 15.3., 29.5., 31.5., 19.6., 21.6.

Am Freitag, dem 12.4. findet die VO von 13:00-14:00 statt !!!

Vorlesungsvideos:

https://owncloud.tuwien.ac.at/index.php/s/vX4Jux1iaMvCyJE
https://owncloud.tuwien.ac.at/index.php/s/M5QMbUXiPmKHZGI
https://owncloud.tuwien.ac.at/index.php/s/pQkR5ng7cSGbRLk
https://owncloud.tuwien.ac.at/index.php/s/gYFRyfTI5BVblxg
https://owncloud.tuwien.ac.at/index.php/s/ivE5bV1NSQflt07
https://owncloud.tuwien.ac.at/index.php/s/UCkphLPr7VzUgkn
https://owncloud.tuwien.ac.at/index.php/s/rZp6os2ewEhnG2q
https://owncloud.tuwien.ac.at/index.php/s/sbJpdAR97dmhgq6
https://owncloud.tuwien.ac.at/index.php/s/2hCXWMglK0KRdYN
https://owncloud.tuwien.ac.at/index.php/s/W5dcZfow2IJmzUj
https://owncloud.tuwien.ac.at/index.php/s/hjWQPx48AR1Y5lY

Oral exam.