  Let R be a commutative ring and let G be a free R-module with positive rank
e. For any R-submodule E of G we may consider the image of the symmetric
algebra of E by the natural map to the symmetric algebra of G, and then the
graded components E_n of the image, that we call the n-th Rees powers of E. In
this work we prove some asymptotic properties of the modules E_n, which extend
well known similar ones for the case of ideals, among them Burch's inequality
for the analytic spread.
