Abstract
The epimorphic hull H(A) of a commutative semiprime ring A is defined to be the smallest von Neumann regular ring of quotients of A. Let X denote a Tychonoff space. In this paper the structure of H(C(X)) is investigated, where C(X) denotes the ring of continuous real-valued functions with domain X. Spaces X that have a regular ring of quotients of the form C(Y) are characterized, and a “minimum” such Y is found. Necessary conditions for H(C(X)) to equal C(Y) for some Y are obtained.
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