Height one separability and Galois theory in semi-Krull domains (Q1076732)

Let X'(R) be the set of prime ideals of height one in the commutative ring R. An R-algebra S is ''height one separable'' if \(S_ p\) is \(R_ p\)- separable for all \(p\in X'(R)\), and an integrally closed domain R is ''semi-Krull'' if \(R_ p\) is a DVR for all \(p\in X'(R)\) and each \(0\neq x\in R\) is contained in at most finitely many \(p\in X'(R)\). (Krull domains are semi-Krull, but not conversely.) The author constructs a ''height one separable closure'' S for a semi-Krull domain R, and shows that it is unique up to isomorphism. Moreover, there is a Galois correspondence between integrally closed height one strongly separable extensions T of R contained in S and closed subgroups H of finite index in \(Aut_ R(S)\), given in the usual way: \(H\to S^ H\) and \(T\to Aut_ T(S)\).