Prime ideal structure in commutative rings

Abstract

Augustfunctor oî3/t\n if; also, we shall say that Fis a space-preserving functor from 38 to«".It turns out that Spec can be inverted on surprisingly large subcategories of ¡f.At this point, the results of §7 should be read as part of this introduction.In fact, after looking at §1, §2 and the results of §7, the reader can continue and finish the paper (except for the proof of Theorem 9 in §16), and then go back to the technical § §3-6 if he wishes.We note that §16 uses the functorial nature of our constructions to characterize the underlying spaces of preschemes and schemes.