The Maximal Ring Of Quotients Of The Functionally Countable Subalgebra Of C(X)

The Maximal Ring Of Quotients Of The Functionally Countable Subalgebra Of C(X)

In this short note we study the ring of quotients of the functionally countable - subalgera of C(X) (this subalgera denoted by CC(X)). The maximal ring of quotients of CC(X) up to direct limit of rings CC(V), where V ranges over dense open subsets in X, was characterized. Furthermore we showed that for every zero dimensional locally compact Hausdorff space X, we always have QC (X) = Q(υX) = Q(βX). Finally, it is shown that QC (X) = CC(X) if and only if X is CC– embedded in X