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.
Keywords: essential morphism, epimorphic hull
2000 MSC: 18A20, 54C45, 54B30
Theory and Applications of Categories,
Vol. 14, 2005,
No. 2, pp 46-52.