The purpose of this paper is to derive constructive necessary and sufficient conditions for the problem of disturbance decoupling with algebraic output feedback. Necessary and sufficient conditions have also been derived for the same problem with internal stability. The same conditions have also been expressed by the use of invariant zeros. The main tool used is the dual-lattice structures introduced by [G. Basile and G. Marro: Controlled and Conditioned Invariants in Linear System Theory. Prentice Hall, New Jersey 1992.].