The lattice-isometric copies of in quotients of Banach lattices

Let E be a Banach lattice and let M be a norm-closed and Dedekind σ-complete ideal of E. If E contains a lattice-isometric copy of ℓ∞, then E/M contains such a copy as well, or M contains a lattice copy of ℓ∞. This is one of the consequences of more general results presented in this paper.