Lattice of subalgebras in the finitely generated varieties of MV-algebras

In this paper, we use the theory of natural duality to study subalgebra lattices in the finitely generated varieties of MV-algebras. With this tool, we obtain the dual atomicity of these lattices, and characterize the members of these varieties in which every subalgebra is an intersection of maximal subalgebras. Then, we determine the algebras that have a modular or distributive lattice of subalgebras.