  Here we introduce and characterize a new class of le-modules $_{R}M$ where
$R$ is a commutative ring with $1$ and $(M,+,\leqslant,e)$ is a lattice ordered
semigroup with the greatest element $e$. Several notions are defined and
uniqueness theorems for primary decompositions of a submodule element in a
Laskerian le-module are established.
