On the Maximal Ring of Quotients of C(x)

1. Let QiX) denote the maximal ring of quotients (in the sense of Johnson [4] and Utumi [5]) of the ring C(X) of continuous realvalued functions on the completely regular Hausdorff space X, This ring has been studied by Fine, Gillman, and Lambek [ l] and realized by them as the direct limit of the subrings C(V), Va, dense open subset of X (i.e., the union of these C(F)'s, modulo the obvious equivalence relation). From this representation of Q(X), it follows that if X and F have homeomorphic dense open subsets, then Q(X) and Q(Y) are isomorphic. The full converse to this is false (see below). In this note a proof of the following is described.