The prime spectrum of a two-dimensional affine domain
Let A be a two-dimensional domain which is finitely generated as an algebra over a field k. The main theorem of this paper is that the partially ordered sets Spec A and Spec \({\mathbb{Z}}[X]\) are isomorphic if and only if k is contained in the algebraic closure of a finite field. The proof makes use of an axiomatic description of the poset Spec \({\mathbb{Z}}[X]\). (We have let \({\mathbb{Z}}\) denote the integers.)
scientific article; zbMATH DE number 3950669