 If "X" is a vector lattice then a vector sublattice is a vector subspace "F" of "X" such that for all "x" and "y" in "F", formula_2 belongs to "F" (where this supremum is taken in "X").It can happen that a subspace "F" of "X" is a vector lattice under its canonical order but is "not" a vector sublattice of "X".A vector subspace of a Riesz space is called an ideal if it is "solid", meaning if for and , we have