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In this paper we discuss the properties of the biordered set obtained from acomplemented modular lattice and defines an operation using the sandwichelements of the biordered set. Further we describe a biordered subsetsatisfying certain conditions, so that the complemented modular lattice admitsa homogeneous basis. Finally analogous to von Neumann coordinatization theoremwe describe the coordinatization theorem for complemented modular lattice usingthe biordered set of idempotents.

Biordered sets of lattices and homogeneous basis