Modules of reduction number one
Commutative Algebra
2007-05-23 v1
Abstract
Let (A, m) be a Noetherian local ring and N a parameter module in F=A^r and M=N:_F m the socle module of N. In this paper, we shall prove that the module M=N:_F m has a reduction number at most one and hence its Rees algebra R(M) is Cohen-Macaulay, if the base ring A is Cohen-Macaulay of dimension two and the rank of N is greater than or equal to two. This result gives numerous examples of Cohen-Macaulay Rees algebras of modules, which are not integrally closed and not a parameter module.
Cite
@article{arxiv.math/0612741,
title = {Modules of reduction number one},
author = {Futoshi Hayasaka},
journal= {arXiv preprint arXiv:math/0612741},
year = {2007}
}
Comments
15 pages