Contents: Functions of a Topological Space.- Ideals and Z-Filters.- Completely Regular Spaces.- Fixed Ideals. Compact Spaces.- Ordered Residue Class Rings.- The Stone-Czech Compactification.-… Expand

The present paper deals with two distinct, though related, questions, concerning the ring C(X, R) of all continuous real-valued functions on a completely regular topological space X. The first of… Expand

The promise made at the beginning of Chapter 6 that βX is to be used to characterize the maximal ideals in C(X) and in C*(X), will be fulfilled in this chapter. The key to the description of the… Expand

In this and the following paper [2], we are concerned with obtaining conditions on a commutative ring S with identity element in order that every matrix over S can be reduced to an equivalent… Expand

An abstract ring in which all finitely generated ideals are principal will be called an F-ring. Let C(X) denote the ring of all continuous real-valued functions defined on a completely regular… Expand

The proof turns out to be considerably more difficult than anticipated. If we assume the continuum hypothesis (designated [CH]), then we can find such a point p (2.5); however, we do not know whether… Expand

A classical theorem of Steinitz [12, p. 125] states that the characteristic of an algebraically closed field, together with its absolute degree of transcendency, uniquely determine the field (up to… Expand