On Essential Ring Embeddings and the Epimorphic Hull of C(x)
نویسندگان
چکیده
Storrer introduced the epimorphic hull of a commutative semiprime ring R and showed that it is (up to isomorphism) the unique essential epic von Neumann regular extension of R. In the case when R = C(X) with X a Tychonoff space, we show that the embedding induced by a dense subspace of X is always essential. This simplifies the search for spaces whose epimorphic hull is a full ring of continuous functions, and allows us to obtain new examples where this occurs. The main theorem comes close to a characterisation of this phenomenon.
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