In studies conducted to explain the dependence in random elements, the possibility of order between them has been less considered. This issue has created problems in the development and application of dependent random elements, some of which can be reduced by using lattice spaces. For this reason, in the present study, we first introduce Banach lattice random elements and some of their properties, and then, using the order defined in the Banach lattice space, we introduce and characterize negative ordinal dependence. Finally, we examine some limit rules for a sequence of Banach lattice random elements with negative ordinal dependent values, and show the results using simulated lattice random elements.
