Extensions of l-homomorphisms
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.
Publication Source (Journal or Book title)
Rocky Mountain Journal of Mathematics
Aron, E., Hager, A., & Madden, J. (1982). Extensions of l-homomorphisms. Rocky Mountain Journal of Mathematics, 12 (3), 481-490. https://doi.org/10.1216/RMJ-1982-12-3-481