2007-10-08
- Hand out homeworks 2 and 3. Mention that 1 and 2 are due this Friday, October 12.
- Announcement for this week:
- crypto seminar on Wednesday at 4pm by Neal Koblitz about his new controversial paper in the Notices of the AMS. Location TBA in class on Wednesday. You definitely want to be there if you have any interest in crypto.
- today: Dedekind domains; wednesday: sage; friday: Proof of the unique factorization theorem.
Prove that
plan(2f)2007(2d)10(2d)08/latex_7ca7d5eb94b6fde12c12384eddf424ea682cbdfd_p1.png "$O_K$")
is a Dedekind domain. - Define the notion of fractional ideal and "divides" for ideals.
- State some theorems:
- Set of fractional ideals forms a group
- Every ideal divides a product of primes.
- Every ideal factors uniquely as a product of primes.