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Maximal d-Ideals in a Riesz Space

Published online by Cambridge University Press:  20 November 2018

Charles B. Huijsmans  and
Ben de Pagter
Charles B. Huijsmans
Affiliation:
Leiden State University, Leiden, The Netherlands'
Ben de Pagter
Affiliation:
California Institute of Technology, Pasadena, California
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We recall that the ideal I in an Archimedean Riesz space L is called a d-ideal whenever it follows from ƒ ∊ I that {ƒ}dd ⊂ I. Several authors (see [4], [5], [6], [12], [13], [15] and [18]) have considered the class of all d-ideals in L, but the set ℐd of all maximal d-ideals in L has not been studied in detail in the literature. In [12] and [13] the present authors paid some attention to certain aspects of the theory of maximal d-ideals, however neglecting the fact thatℐd, equipped with its hull-kernel topology, is a structure space of the underlying Riesz space L.

The main purpose of the present paper is to investigate the topological properties of ℐd and to compare ℐd to other structure spaces of L, such as the space of minimal prime ideals and the space of all e-maximal ideals in L (where e > 0 is a weak order unit).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 6 , 01 December 1983 , pp. 1010 - 1029
Copyright
Copyright © Canadian Mathematical Society 1983

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