@article {
author = {Carrera, Ricardo E. and Hager, Anthony W.},
title = {A classification of hull operators in archimedean lattice-ordered groups with unit},
journal = {Categories and General Algebraic Structures with Applications},
volume = {13},
number = {1},
pages = {83-104},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.13.1.83},
abstract = {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 $w: {\bf hoW} \longrightarrow {\bf W}^{\bf W}$ obtained as a finite composition of $B$ and $x$ a variable ranging in $\bf hoW$. The set of these,``Word'', is in a natural way a partially ordered semigroup of size $6$, order isomorphic to ${\rm F}(2)$, the free $0-1$ distributive lattice on $2$ generators. Then, $\bf hoW$ is partitioned into $6$ disjoint pieces, by equations and inequations in words, and each piece is represented by a characteristic order-preserving quotient of Word ($\approx {\rm F}(2)$). Of the $6$: $1$ is of size $\geq 2$, $1$ is at least infinite, $2$ are each proper classes, and of these $4$, all quotients are chains; another $1$ is a proper class with unknown quotients; the remaining $1$ is not known to be nonempty and its quotients would not be chains.},
keywords = {lattice-ordered group,Archimedean,weak unit,bounded monocoreflection,essential extension,hull operator,partially ordered semigroup},
url = {https://cgasa.sbu.ac.ir/article_87552.html},
eprint = {https://cgasa.sbu.ac.ir/article_87552_9aa6961ac859a3c87241c8124af70410.pdf}
}