Sally Modules and Reduction Numbers of Ideals
Commutative Algebra
2015-05-19 v1
Abstract
We study the relationship between the reduction number of a primary ideal of a local ring relative to one of its minimal reductions and the multiplicity of the corresponding Sally module. This paper is focused on three goals: (i) To develop a change of rings technique for the Sally module of an ideal to allow extension of results from Cohen-Macaulay rings to more general rings. (ii) To use the fiber of the Sally modules of almost complete intersection ideals to connect its structure to the Cohen-Macaulayness of the special fiber ring. (iii) To extend some of the results of (i) to two-dimensional Buchsbaum rings. Along the way we provide an explicit realization of the S_2-fication of arbitrary Buchsbaum rings.
Cite
@article{arxiv.1505.04687,
title = {Sally Modules and Reduction Numbers of Ideals},
author = {Laura Ghezzi and Shiro Goto and Jooyoun Hong and Wolmer Vasconcelos},
journal= {arXiv preprint arXiv:1505.04687},
year = {2015}
}