Rings of Quotients of Rings of Functions

From the original PREFACE: The rings of quotients recently introduced by Johnson and Utumi are applied to the ring C (X) of all continuous real-valued functions on a completely regular space X. Let Q (X) denote the maximal ring of quotients of C (X) ; then Q (X) may be realized as the ring of all continuous functions on the dense open sets of X (modulo an obvious equivalence relation). In special cases (e. g. , for metric X), Q (X) reduces to the classical ring of quotients of C (X) (formed with respect to the regular elements), but in general, the classical ring is only a proper sub-ring of Q (X).