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 
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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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