Some asymptotic properties of the Rees powers of a module
Commutative Algebra
2007-05-23 v1
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 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.
Cite
@article{arxiv.math/0408351,
title = {Some asymptotic properties of the Rees powers of a module},
author = {Ana L. Branco Correia and Santiago Zarzuela},
journal= {arXiv preprint arXiv:math/0408351},
year = {2007}
}
Comments
13 pages