On the Flatness of the Epimorphic Hull of a Ring of Continuous Functions
For commutative semiprime rings R, the classical ring of quotients Q ci (R) is R-flat, but the epimorphic hull E(R) need not be. An example due to Quentel shows that E(R) can be flat and still not coincide with Q ci (R). In Proposition 7 below we show that such behaviour is excluded for rings of the form C(X). A related question is addressed, and we characterize, for any cardinal α, the Tychonoff spaces X for which all ideals of C(X) are essentially α-generated.
KeywordsPrime Ideal Regular Ring Semiprime Ring Nonempty Open Subset Minimal Prime Ideal
Unable to display preview. Download preview PDF.
- [B]N. Bourbaki, Eléments de mathématique. Fasc. XXVII: Algèbre commutative; chapitre 1: Modules plats; chapitre 2: Localisation; (1961) Hermann, Paris.Google Scholar
- [HM2]A. W. Hager and J. Martinez, The ring of a-quotients. To appear; Alg. Universalis.Google Scholar
- [H]R. Hodel, Cardinal Functions, I. Handbook of Set-Theoretic Topology (1984) North-Holland, Amsterdam, 1–61.Google Scholar