The space of minimal prime ideals of a commutative ring

Abstract

Introduction. Of the various spaces of ideal of rings that have been studied (see [1 ], for example) we are focusing attention on the space of minimal prime ideals because of its special role in the case of rings of continuous functions. For the simplest manifestation of this role, consider the compact space N* obtained from the discrete space of positive integers N by adjoining a single point, o. In the ring C(N*) of all continuous real-valued functions on N*, the maximal ideals are very easy to describe. They are in one-one correspondence with the points of N*, and are given by