Some asymptotic properties of the Rees powers of a module
Abstract
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 En of the image, that we call the n-th Rees powers of E. In this work we prove some asymptotic properties of the modules En, which extend well known similar ones for the case of ideals, among them Burch's inequality for the analytic spread.
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