a classification of hull operators inarchimedean lattice-ordered groups withunit

The category, or class of algebras, in the title is denoted byw. a hull operator (ho) in w is a reflection in the category consisting ofw objects with only essential embeddings as morphisms. the proper classof all of these is how. the bounded monocoreflection in w is denoted b.we classify the ho’s by their interaction with b as follows. a “word” is afunction w : how −! w^w obtained as a finite composition of b and x avariable ranging in how. the set of these,“word”, is in a natural way apartially ordered semigroup of size 6, order isomorphic to f(2), the free 0−1distributive lattice on 2 generators. then, how is partitioned into 6 disjointpieces, by equations and inequations in words, and each piece is representedby a characteristic order-preserving quotient of word ( f(2)). of the 6: 1is of size ≤ 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 bechains.