Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585313120200701A classification of hull operators in archimedean lattice-ordered groups with unit831048755210.29252/cgasa.13.1.83ENRicardo E. CarreraDepartment of Mathematics, Nova Southeastern University, 3301 College Ave., Fort Lauderdale, FL, 33314, USA.Anthony W. HagerDepartment of Mathematics and CS, Wesleyan University, Middletown, CT 06459.Journal Article20191026The 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.https://cgasa.sbu.ac.ir/article_87552_9aa6961ac859a3c87241c8124af70410.pdf