proof of finite extensions of Dedekind domains are Dedekind
We procede by splitting the proof up into the separable and purely inseparable cases. Letting consist of all elements of which are separable over , then is a separable extension and is a purely inseparable extension.
First, the integral closure of in is a Dedekind domain (see proof of finite separable extensions of Dedekind domains are Dedekind). Then, as is integrally closed and contains , it is equal to the integral closure of in and, therefore, is a Dedekind domain (see proof of finite inseparable extensions of Dedekind domains are Dedekind).
|Title||proof of finite extensions of Dedekind domains are Dedekind|
|Date of creation||2013-03-22 18:35:44|
|Last modified on||2013-03-22 18:35:44|
|Last modified by||gel (22282)|