The lattice copies of ℓ∞(Γ)/c0(Γ) in a quotient of a Banach lattice

Let E be a Dedekind σ-complete Banach lattice, let Ea denote the order continuous part of E, andsuppose that Ea is order dense in E. If E contains a lattice copy of ℓ∞ (equivalently, E ≠ a) then E/Ea contains a lattice copy of ℓ∞/c0, and hence a lattice-isometric copy of ℓ∞. This is one of the consequences of more general results presented in this paper.