Equalities Among Various Rings Of Quotients Of The Functionally Countable Subring Of C(X)

In this short note we state the conditions that satisfy the equality of rings of quotients of the functionally countable subalgera of C(X). In particular, it is shown that the classical ring of quotients and the maximal ring of quotients of this algebra are equivalent if and only if corresponding their bounded subrings are equivalent. Finally it is shown that for second countable zero-dimensional space X, two above mentioned rings are the same.

Keywords:

zero-dimensional space , Cc-embedding , c-completely regular space , functionally countable subalgebra