Hi! Let A be a subring of a ring which is integral over . Then the following assertions hold:

(i) is integral over

(ii) Let be an ideal of and define , then is integral over .

ad (i)

Let (polynomial with degree n). I want to show that is a finitely generated A[X]-module. I guess that generates . Is this the right way? If yes, is it the right execution?

ad (ii)

Here, i have the following idea: Let and be any representative of this equivalence class. As is integer over , there exists , so that . Let be the canonical projection , then it follows that , therefore .

But is this polynomial now in ?

Has somebody got answers or ideas?

Banach