Localization and test exponents for tight closure
交换代数
2007-05-23 v1
摘要
In this paper we study various equivalent conditions for tight closure to commute with localization. If N is a submodule of a finitely generated module M over a Noetherian commutative ring of characteristic p, then a test exponent for c,N,M is defined to be a power q' of p such that u is in the tight closure of N in M whenever cu^q is in the qth Frobenius power of N for some q \ge q'. We prove that that a test exponent for a locally stable test element c and for N,M as above exists if and only if the tight closure of N in M commutes with localization. Other equivalent conditions are given for tight closure to commute with localization.
引用
@article{arxiv.math/0211173,
title = {Localization and test exponents for tight closure},
author = {Melvin Hochster and Craig Huneke},
journal= {arXiv preprint arXiv:math/0211173},
year = {2007}
}