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Certain extensions and factorizations of α-complete homomorphisms in archimedean lattice-ordered groups

Part of: Topological linear spaces and related structures General theory of categories and functors Ordered structures

Published online by Cambridge University Press:  09 April 2009

Anthony W. Hager  and
Ann Kizanis
Anthony W. Hager
Affiliation:
Mathematics Department Wesleyan UniversityMiddletown, CT 06459, USA
Ann Kizanis
Affiliation:
Mathematics Department Western New England CollegeSpringfield, MA 01119, USA
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Abstract

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As a consequence of general principles, we add to the array of ‘hulls’ in the category Arch (of archimedean ℓ-groups with ℓ-homomorphisms) and in its non-full subcategory W (whose objects have distinguished weak order unit, whose morphisms preserve the unit). The following discussion refers to either Arch or W. Let α be an infinite cardinal number or ∞, let Homα; denote the class of α-complete homomorphisms, and let R be a full epireflective subcategory with reflections denoted rG: G → rG. Then for each G, there is rαG ∈ Homα (G, R) such that for each ϕ ∈ Homα (G, R), there is unique with . Moreover if every rG is an essential embedding, then, for every α and every G, rαG = rG, and every Homα. If and R consists of all epicomplete objects, then every Homw1. For α = ∞, and for any R, every Hom∞.

MSC classification

Secondary: 06F20: Ordered abelian groups, Riesz groups, ordered linear spaces 18A20: Epimorphisms, monomorphisms, special classes of morphisms, null morphisms 18A32: Factorization of morphisms, substructures, quotient structures, congruences, amalgams 46A40: Ordered topological linear spaces, vector lattices
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 62 , Issue 2 , April 1997 , pp. 239 - 258
Copyright
Copyright © Australian Mathematical Society 1997

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