On the Embedding into a Ring of an Archimedean ι-Group
Copyright policy )On the Embedding into a Ring of an Archimedean ι-Group
We shall prove the following about the “ringification” ρA of [2] and [5] of an archimedean l-group A: (a) Any “minimal ring” containing A is ρA; (b) A ↦ ρA is a reflector; (c) ρA need not be laterally complete when A is. These constitute the solutions to the problems posed in [2] by Paul Conrad.1. The embedding into a ring. Let be the category which has objects archimedean l-groups A with distinguished positive weak unit eA, and morphisms l-group homomorphisms h: A → B with h(eA) = eB. Let be the category with objects archimedean f-rings R with identity 1R which is a weak unit, and morphisms l-ring homomorphisms h: R → S with h(lR) = 1S.
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Ordered rings, algebras, modules, Archimedean Lattice-Ordered Group with a Weak Unit, F- Ring Homomorphism, Minimal F-Ring, Ordered abelian groups, Riesz groups, ordered linear spaces
Ordered rings, algebras, modules, Archimedean Lattice-Ordered Group with a Weak Unit, F- Ring Homomorphism, Minimal F-Ring, Ordered abelian groups, Riesz groups, ordered linear spaces
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