Bounded Noetherian Prime Rings of Injective Dimension One

Abstract

<p>This thesis studies the maximal ideals and minimal overrings of the rings of the title. It is shown that then maximal ideals are segregated into projective and non-projectives with no interplay between these classes. Moreover, the projective maximal ideals behave as though the ring were hereditary.</p> <p>The maximal spectrum of minimal equivalent orders is calculated in terms of that of R. This enables a comparison of their link-graphs (they are almost the same) and a characterization of when a minimal equivalent order also has the attributes of the title. This inductive property is shown to be preserved by the "cycle map" as well as passing up to the minimal equivalent order itself.</p>