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Information Journal Paper

Title

ON Z-IDEALS OF POINTFREE FUNCTION RINGS

Pages

  657-675

Keywords

Abstract

 Let L be a completely regular FRAME and RL be the ring of continuous real-valued functions on L. We show that the lattice Zid (RL) of Z-IDEALs of RL is a normal coherent Yosida FRAME, which extends the corresponding C (X) result of Martinez and Zenk. This we do by exhibiting Zid (RL) as a quotient of Rad (RL), the FRAME of radical IDEALs of RL. The saturation quotient of Zid (RL) is shown to be isomorphic to the Stone-Cech compactification of L. Given a morphism h: L®M in CRegFrm, Zid creates a coherent FRAME homomorphism Zid (h): Zid (RL)®Zid (RM) whose right adjoint maps as (Rh)-1, for the induced ring homomorphism Rh: RL®RM. Thus, Zid (h) is an s-map, in the sense of Martinez [18], precisely when R (h) contracts maximal IDEALs to maximal IDEALs.

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    APA: Copy

    DUBE, THEMBA, & IGHEDO, OGHENETEGA. (2014). ON Z-IDEALS OF POINTFREE FUNCTION RINGS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 40(3), 657-675. SID. https://sid.ir/paper/643607/en

    Vancouver: Copy

    DUBE THEMBA, IGHEDO OGHENETEGA. ON Z-IDEALS OF POINTFREE FUNCTION RINGS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2014;40(3):657-675. Available from: https://sid.ir/paper/643607/en

    IEEE: Copy

    THEMBA DUBE, and OGHENETEGA IGHEDO, “ON Z-IDEALS OF POINTFREE FUNCTION RINGS,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 40, no. 3, pp. 657–675, 2014, [Online]. Available: https://sid.ir/paper/643607/en

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