A Banach lattice E (over the field of reals) is said to be injective if, for every Banach lattice G, every closed linear sublattice F of G and every positive linear operator u: F--*E, there is a positive linear extension v: G . E with IIv[I = Ilull. This definition of injectivity is the standard one if we agree to work with the category Balatl of Banach lattices and positive linear contractions, and to take as embeddings all isometric linear lattice homomorphisms. The concept was first examined by Lotz [7], who showed that lattices of the following classes are injective: (I) ~(S), where S is stonian (that is, compact and extremally disconnected); (II) (AL)-spaces. It is the second of these which shows that there really are significant differences between this theory and the corresponding ideas for Banach spaces. We recall that the Nl-spaces, which are the injective objects in the category Ban~ of Banach spaces and linear contractions, can be characterized in a number of ways (see for instance p. 160 of [6]):