An l-ideal A of an l-group G
is closed if x ∈ A whenever x = ∨ai,0 ≤ ai∈ A. The intersection of any
collection of closed l-ideals of G is again a closed l-ideal of G. Hence the
set 𝒦(G) of all closed l-ideals of G is a complete lattice under inclusion.
In the present paper this lattice is studied, as well as l-group extensions
which preserve it. A common generalization of the essential closure of an
archimedean l-group and the Hahn closure of a totally-ordered abelian group is
obtained.