  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 $Q(X)$.
