Abstract
This paper is concerned with the classes\(WP, P\) and\(SP\) of weakly projectable, projectable, and strongly projectablel-groups (lattice-ordered groups). It is shown that the members of\(P\)] and\(SP\) can be characterized purely in terms of their order structures, and these characterizations are used in establishing, among other things, that lattice isomorphisms preserve projectability and strong projectability. Further characterizations in terms of the lattice of convexl-subgroups are also given. Additional results include the following: The existence of an indecomposable, weakly projectable archimedeanl-group; the fact that the\(WP\)-radical of a laterally completel-group is a conditionally orthocompletel-group; and finally, the result that the\(SP\)-radical of anl-groupG contains every strongly projectablel-group that is large inG.
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In memoriam Jürgen Schmidt
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Tsinakis, C. Projectable and strongly projectable lattice-ordered groups. Algebra Universalis 20, 57–76 (1985). https://doi.org/10.1007/BF01236806
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DOI: https://doi.org/10.1007/BF01236806