  In this paper, we present a simple lattice-theoretic characterization for
affine buildings of type A. We introduce a class of modular lattices, called
uniform modular lattices, and show that uniform modular lattices and affine
buildings of type A constitute the same object. This is an affine counterpart
of the well-known equivalence between projective geometries ($\simeq$
complemented modular lattices) and spherical buildings of type A.
