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On the Flatness of the Epimorphic Hull of a Ring of Continuous Functions

  • R. Raphael
  • R. G. Woods
Part of the Developments in Mathematics book series (DEVM, volume 7)

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.

Keywords

Prime Ideal Regular Ring Semiprime Ring Nonempty Open Subset Minimal Prime Ideal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • R. Raphael
    • 1
  • R. G. Woods
    • 2
  1. 1.Department of MathematicsConcordia UniversityMontrealCanada
  2. 2.Department of MathematicsUniversity of ManitobaWinnipegCanada

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