Abstract
A complemented l-group G is one in which to each a ∈ G there corresponds a b ∈ G so that |a|⋏|b|=0, while |a|⋎|b| is a unit of G. For projectable l-groups this is so precisely when the group possesses a unit.
The article introduces the notion of complementation, and the situation for projectable l-groups is analyzed in some detail; in particular, it is shown that any projectable l-group having a projectable complementation in which it is convex has a unique maximal one of this kind.
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Communicated by A. M. W. Glass
A portion of this research was carried out while this author was a Stauffer Visiting Professor at the University of Kansas during the year 1986–87. He thanks his colleagues in mathematics at that institution for their hospitality.
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Conrad, P., Martinez, J. Complementing lattice-ordered groups: The projectable case. Order 7, 183–203 (1990). https://doi.org/10.1007/BF00383766
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DOI: https://doi.org/10.1007/BF00383766