Geodesic
On essential ring embeddings and the epimorphic hull of C(X)
Theory and applications of categories, Tome 14 (2005), pp. 46-52

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Classification : 18A20, 54C45, 54B30
Keywords: essential morphism, epimorphic hull 
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     title = {On essential ring embeddings and the epimorphic hull of {C(X)}},
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R. Raphael; R.G. Woods. On essential ring embeddings and the epimorphic hull of C(X). Theory and applications of categories, Tome 14 (2005), pp. 46-52. http://geodesic.mathdoc.fr/item/TAC_2005_14_a1/