New York Journal of Mathematics
Volume 22 (2016) 351-361


Themba Dube

A note on lattices of z-ideals of f-rings

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Published: April 3, 2016
Keywords: f-ring, z-ideal, coherent frame, proper map, functor, natural transformation
Subject: Primary: 06F25; Secondary: 06D22, 13A15, 18A05

The lattice of z-ideals of the ring C(X) of real-valued continuous functions on a completely regular Hausdorff space X has been shown by Martinez and Zenk to be a complete Heyting algebra with certain properties. We show that these properties are due only to the fact that C(X) is an f-ring with bounded inversion. This we do by studying lattices of algebraic z-ideals of abstract f-rings with bounded inversion.


The author acknowledges funding from the National Research Foundation of South Africa through a research grant with Grant No. 93514.

Author information

Department of Mathematical Sciences, University of South Africa, P. O. Box 392, 0003 Pretoria, South Africa.