z∘-filters and related ideals in C(X)

Document Type : Research Paper

Author

Shahid Chamran University of Ahvaz

Abstract

In this article we introduce the concept of z∘-filter on a topological space X. We study and investigate the behavior of z∘-filters and compare them  with corresponding ideals, namely, z∘-ideals of C(X),  the ring of real-valued continuous functions on a completely regular Hausdorff space X. It is observed that X is a compact space if and only if every z∘-filter is ci-fixed. Finally, by using  z∘-ultrafilters, we prove that any arbitrary product of i-compact spaces is i-compact.

Keywords

References

[1] F. Azarpanah, On almost P-spaces, Far East J. Math. Sci., Special Volume, 121{132 (2000).
[2] F. Azarpanah, O.A.S. Karamzadeh and A. Rezaei Aliabad, On z-ideals in C(X), Fund. Math., 160, 15{25 (1999).
[3] F. Azarpanah, O.A.S. Karamzadeh and A. Rezaei Aliabad, On ideal consisting entirely of zerodivisor, Comm. Algebra, 28(2), 1061{1073 (2000).
[4] F. Azarpanah and M. Karavan, On nonregular ideals and z-ideal in C(X), Cech. Math. J., 55(130), 397{407 (2005).
[5] F. Azarpanah and R. Mohamadian, pz-ideals and pz-ideals in C(X), Acta. Math. Sinica., English Series, 23,
989{996 (2007).
[6] R. Engelking, General Topology, PWN-Polish Sci Publ, 1977.
[7] L. Gillman and M. Jerison, Rings of Continuous Functions, Springer-Verlag, New York, 1976.
[8] G. Mason, z-ideals and prime ideals, J. Algebra, 26: 280{297 (1973).
Algebraic Structures and Their Applications
Volume 2, Issue 2
November 2015
Pages 57-66

Files

Share

How to cite

Statistics