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Algebraic Number Theory

The course will be given by prof. Günter Lettl (Graz University) in blocked form.

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.

Dates

10 Oktober 2011, 10:15 - 12:45 Uhr, HF9905
4 November 2011, 12:00 - 14:30 Uhr, BA9907
11 November 2011, 12:00 - 14:30 Uhr, K223B
14 November 2011, 10:15 - 12:45 Uhr, K009D
25 November 2011, 12:00 - 14:30 Uhr, K223B
28 November 2011, 10:15 - 12:45 Uhr, K009D
9 December 2011, 12:00 - 14:30 Uhr, K223B
12 December 2011, 10:15 - 12:45 Uhr, K009D
13 January 2012, 12:00 - 14:30 Uhr, K223B
16 January 2012, 10:15 - 12:45 Uhr, K009D

 

 For details see http://www.risc.jku.at/education/courses/ws2011/AlgZT/