Convex vector lattices and l-algebras

DOI10.1016/0166-8641(81)90024-9zbMath0458.06012OpenAlexW2065604380MaRDI QIDQ1151415

Anthony W. Hager, Eleanor R. Aron

Publication date: 1981

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0166-8641(81)90024-9

zbMATH Keywords

Archimedean Riesz spaceconvex reflectionconvex Riesz spacesRiesz ideal

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Algebraic properties of function spaces in general topology (54C40) Ordered rings, algebras, modules (06F25) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) Topological representations of algebraic systems (54H10)

Related Items (17)

Bounded equivalence of hull classes in Archimedean lattice-ordered groups with unit. ⋮ The \(H\)-closed monoreflections, implicit operations, and countable composition, in Archimedean lattice-ordered groups with weak unit ⋮ Patch-generated frames and projectable hulls ⋮ The completeness characterization of \(C(\mathcal{L})\), \(\mathcal{L}\) a locale ⋮ Extremal units in an Archimedean Riesz space ⋮ Some modifications of hull operators in Archimedean lattice-ordered groups with weak unit ⋮ Relative uniform completeness and order-convex representations of Archimedean \(\ell \)-groups and \(f\)-rings ⋮ Algebraic extensions of an archimedean lattice-ordered group. I ⋮ A new characterization of the continuous functions on a locale ⋮ The inversion characterizations of \(C(\mathcal{L})\) for a locale \(\mathcal{L} \) ⋮ Unique a-closure for some ℓ-groups of rational valued functions ⋮ Rigid extensions of ℓ-groups of continuous functions ⋮ Weakly least integer closed groups ⋮ Functorial approximation to the lateral completion in archimedean lattice-ordered groups with weak unit ⋮ The Relatively Uniform Completion, Epimorphisms and Units, in Divisible Archimedean L-Groups ⋮ Functorial rings of quotients. III: The maximum in Archimedean \(f\)-rings ⋮ On the localic Yosida representation of an archimedean lattice ordered group with weak order unit

Cites Work

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• Extremal units in an Archimedean Riesz space
• On the structure of a class of archimedean lattice-ordered algebras
• Residue class fields of lattice-ordered algebras
• Order-Cauchy Completions of Rings and Vector Lattices of Continuous Functions
• The Additive Group of an f-ring
• Shorter Notes: A Theorem on C ∗ -Embedding
• On the Embedding into a Ring of an Archimedean ι-Group
• Maximal lattice-ordered algebras of continuous functions
• Inversion in a class of lattice-ordered algebras

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