Lecture 19. Prime ideals in integral extensions
Автор: Yuly Billig
Загружено: 2022-05-15
Просмотров: 234
0:00 Dedekind Theorem
4:19 Basic setup: integral elements in Galois extensions
8:43 Galois group action on the ring of integral elements
14:05 Ideals in a ring extension lying over ideals in the base ring
14:57 Example: prime ideals in Z[sqrt(-5)]
20:21 Example: prime ideals in the ring of functions on an elliptic curve
29:58 Theorem: prime ideals can always be lifted
39:50 Prime ideals in an extension lying over the same ideal in the base ring can not be nested
In this lecture we study prime ideals in integral extensions of rings. We show that for every prime ideal P of the base ring, there exists a prime ideal Q in the integral extension, lying over P.
This is a lecture in a graduate course "Groups and Galois Theory".
Here is the complete playlist for this course:
• Groups and Galois Theory (remastered)
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