We also define the notion of strongly algebraically closed lattices and we show that a q′-compact complete boolean lattice is strongly algebraically closed. <...> Keywords: existentially and algebraically closed lattices, strongly algebraically closed lattices, equationally noetherian lattice, complete Boolean algebras. <...> Introduction Suppose L is an algebraic language and A is an algebra of type L. If we attach the elements of algebraically closed algebra in the class X. Equivalently, A is existentially closed in X, if and only if every finite set of equations and inequations with coefficients from A, which is solvable in some B ∈ X containing A, already has a solution in A itself. <...> Similarly A is algebraically closed in X, if and only if every finite set of equations with coefficients from A, which is solvable in some B ∈ X containing A, already has a solution in A. Many articles have already been published concerning the existentially and algebraically closed algebras in several algebraic structures. <...> In this paper, we focus on distributive lattices. <...> Already, in [4] J. Schmid proved that in the class of distributive lattices, a lattice A is algebraically closed if and only if, it is boolean. <...> Schmid asked about the situation in which a distributive lattice is strongly algebraically closed. <...> Note that we say that an algebra A is strongly algebraically closed in a class X, if every set of equations (finite or infinite) with coefficients from A, which is solvable in some B ∈ X containing A, already has a solution in A. In the case of lattices, it is easy to see that such a distributive lattice must be a complete boolean lattice. <...> The organization of the paper is as follows: in Section 1, we show that if a class X of lattices is inductive and closed under elementary sublattices, then every element of X has an extension which is existentially closed in X. In fact, this result is not new and at least a version of it for classes of groups is presented in [5]. <...> However, in our version, the assumption of being closed under elementary substructures is applied instead of the stronger hypothesis of being closed under substructures. ∗a-molkhasi@tabrizu.ac.ir ⃝ Siberian Federal University <...>