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It is shown that, in abelian l-groups, each morphism to a complete vector lattice extends over any majorizing embedding. This extends a result of the first author for Archimedean f-algebras with identity, and the recent Luxemburg-Schep theorem for vector lattices, and solves a problem of Conrad and McAlister. The proof presented here differs substantially from the Luxem- burg-Schep proof. Ours uses the Yosida representation and Gleason’s theorem on topological projectivity—this is novel, and seems relatively economical and transparent. The l-group theorem is shown to imply, and with some modestly categorical machinery, to be implied by, certain similar statements in subcategories of l-groups. © 1982 Rocky Mountain Mathematics Consortium.

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Rocky Mountain Journal of Mathematics

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