Quotient-Like Extension of Rings of Functions

Abstract

<p>In this thesis we study the quotient-like extensions of the rings of all real continuous functions on a topological space previously considered by Fine-Gillman-Lambek and certain generalizations of these. In particular we obtain a result on the absence of real maximal ideals in certain such rings; a connection between the maximal ideal spaces or such rings and projective covers of compact Hausdorff spaces; and a useful description of the relationship between the quotient-like extensions of rings of real functions and their complex counterpart.</p>