proof of Kummer theory
and thus for , we have for some . Define a map
Since , each root of unity is fixed by . Then for ,
so that and is a homomorphism. The kernel of the map consists of all elements of which fix , so that is injective and we are done.
- 1 Dummit, D., Foote, R.M., Abstract Algebra, Third Edition, Wiley, 2004.
- 2 Kaplansky, I., Fields and Rings, University of Chicago Press, 1969.
|Title||proof of Kummer theory|
|Date of creation||2013-03-22 18:42:07|
|Last modified on||2013-03-22 18:42:07|
|Last modified by||rm50 (10146)|