Abstract
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.
The authors thank the NSERC (Canada) for its support. The first author thanks the conference organizer, Jorge Martinez, for support and manifold conference arrangements.
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Raphael, R., Woods, R.G. (2002). On the Flatness of the Epimorphic Hull of a Ring of Continuous Functions. In: Martínez, J. (eds) Ordered Algebraic Structures. Developments in Mathematics, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3627-4_17
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DOI: https://doi.org/10.1007/978-1-4757-3627-4_17
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