Representation of $H$-closed monoreflections in archimedean $ell$-groups with weak unit
نویسندگان
چکیده
منابع مشابه
Archimedean Unital Groups with Finite Unit Intervals
Let G be a unital group with a finite unit interval E, let n be the number of atoms in E, and let κ be the number of extreme points of the state spaceΩ(G). We introduce canonical order-preserving group homomorphisms ξ : Zn → G and ρ : G → Zκ linking G with the simplicial groups Zn and Zκ . We show that ξ is a surjection and ρ is an injection if and only if G is torsion-free. We give an explicit...
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The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflection in $bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function ...
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We prove that in the category of achimedean lattice-ordered groups with weak unit there is no homomorphism-closed monoreflection strictly between the strongest essential monoreflection (the so-called “closure under countable composition”) and the strongest monoreflection (the epicompletion). It follows that in the category of regular σframes, the only non-trivial monoreflective subcategory that...
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ژورنال
عنوان ژورنال: Categories and General Algebraic Structures with Application
سال: 2018
ISSN: 2345-5853,2345-5861
DOI: 10.29252/cgasa.9.1.1