Some asymptotic properties of the Rees powers of a module

摘要

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