exercise 1/25/2018

hi regarding the exercise last time : $\bigvee \sigma (P) + \bigvee \sigma(P') = B$, where P, P' are defined as maximal ideals of the integral closure of B. $\sigma$ is the automorphism of $B$.

by prop1.11(b) of atiyah mcdonald , $\bigvee \sigma (P)$ and $\bigvee \sigma(P') $ are maxima ideals. by assumption in notes that P and P' are in different orbits, it follows that sum of 2 different maximal ideals is the whole ring $B$