Lecture 22. Ideal Class Group скачать в хорошем качестве

Lecture 22. Ideal Class Group

0:00 Theorem: Every ideal in a Dedekind domain has a unique factorization in a product of prime ideals 9:15 Factorization of a principal ideal generated by 7 in the ring Z[sqrt(-5)] 14:26 Theorem: Integral elements in a Galois extension form a Dedekind domain 21:02 Example: Z[sqrt(-5)] is a Dedekind domain 23:05 Example: Polynomial functions on an elliptic curve form a Dedekind domain 25:10 Ideal Class Group 29:12 Computations in the Ideal Class Group of an elliptic curve 46:12 Applications to the public key cryptography In this lecture we show that Dedekind domains may be constructed by taking the ring of integral elements in a Galois extension. We prove the factorization theorem for ideals in a Dedekind domain. Finally we introduce an important construction of the Ideal Class Group and give examples of computations in the Ideal Class Group corresponding to an elliptic curve. This is the final lecture in a graduate course "Groups and Galois Theory". Here is the complete playlist for this course:    • Groups and Galois Theory (remastered)