The prime spectrum of a two-dimensional affine domain

Abstract

From a distance, the two partially ordered sets spec Z[x] and spec Q[x, y] appear rather similar: They each have a unique minimal element and denumerable sets of elements of heights one and two. Moreover, there are several restrictions placed on the orderings by the fact that both rings are Noetherian. We will show that the partial ordering of spec7/[x] is much simpler than that of specQ[x,y]. In fact, U= spec Z[x] is characterized among countable partially ordered sets by the follow