Convex isomorphism of $Q$-lattices

Abstract

V. I. Marmazejev introduced in [3] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which the lattice are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim this paper is to generalize this concept to the $q$-lattices defined in [2] and to characterize the convex isomorphic $q$-lattices.