Rings of Continuous Functions in Which Every Finitely Generated Ideal is Principal

@inproceedings{Gillman2010RingsOC,
title={Rings of Continuous Functions in Which Every Finitely Generated Ideal is Principal},
author={Leonard Gillman and Melvin Henriksen},
year={2010}
}

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 (Hausdorff) space X. This paper is devoted to an investigation of those spaces X for which C(X) is an F-ring. In any such study, one of the problems that arises naturally is to determine the algebraic properties and implications that result from the fact that the given ring is a ring of functions… CONTINUE READING