A class of ideals in intermediate rings of continuous functions


  • Sagarmoy Bag University of Calcutta
  • Sudip Kumar Acharyya University of Calcutta
  • Dhananjoy Mandal University of Calcutta




P-space, almost P-space, UMP-space, z-ideal, zâ—¦-ideal, ƷA-ideal


For  any  completely  regular  Hausdorff  topological  space X,  an  intermediate  ring A(X) of  continuous  functions  stands  for  any  ring  lying between C∗(X) and C(X).  It is a rather recently established fact that if A(X) ≠ C(X), then there exist non maximal prime ideals in A(X).We offer an alternative proof of it on using the notion of zâ—¦-ideals.  It is realized that a P-space X is discrete if and only if C(X) is identical to the ring of real valued measurable functions defined on the σ-algebra β(X) of all Borel sets in X.  Interrelation between z-ideals, zâ—¦-ideal and ƷA-ideals in A(X) are examined.  It is proved that within the family of almost P-spaces X, each ƷA -ideal in A(X) is a zâ—¦-ideal if and only if each z-ideal in A(X) is a zâ—¦-ideal if and only if A(X) = C(X).


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Author Biographies

Sagarmoy Bag, University of Calcutta

Department of Pure Mathematics

Sudip Kumar Acharyya, University of Calcutta

Department of Pure Mathematics

Dhananjoy Mandal, University of Calcutta

Department of Pure Mathematics


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How to Cite

S. Bag, S. K. Acharyya, and D. Mandal, “A class of ideals in intermediate rings of continuous functions”, Appl. Gen. Topol., vol. 20, no. 1, pp. 109–117, Apr. 2019.