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Periodica Mathematica Hungarica

, Volume 31, Issue 2, pp 105–112 | Cite as

Essential ideals inC(X)

  • F. Azarpanah
Article

Abstract

It is shown thatX is finite if and only ifC(X) has a finite Goldie dimension. More generally we observe that the Goldie dimension ofC(X) is equal to the Souslin number ofX. Essential ideals inC(X) are characterized via their corresponding z-filters and a topological criterion is given for recognizing essential ideals inC(X). It is proved that the Fréchet z-filter (cofinite z-filter) is the intersection of essential z-filters. The intersection of idealsOx wherex runs through nonisolated points inX is the socle ofC(X) if and only if every open set containing all nonisolated points is cofinite. Finally it is shown that if every essential ideal inC(X) is a z-ideal thenX is a P-space.

Mathematics subject classification numbers

1991. Primary 54C40 Secondary 13A18 

Key words and phrases

Socle P-space Fréchet-filter essential ideal annihilator nowhere dense Goldie dimension Souslin number 

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Copyright information

© Akadémiai Kiadó 1995

Authors and Affiliations

  • F. Azarpanah
    • 1
  1. 1.Department of MathematicsAhvaz UniversityAhvazIran

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