An upper bound on the reduction number of an ideal
Commutative Algebra
2007-12-03 v1
Abstract
Let A be a commutative ring and I an ideal of A with a reduction Q. In this paper we give an upper bound on the reduction number of I with respect to Q, when a suitable family of ideals in A is given. As a corollary it follows that if some ideal J containing I satisfies J^2 = QJ, then I^{v + 2} = QI^{v + 1}, where v denotes the number of generators of J / I as an A-module.
Cite
@article{arxiv.0711.4880,
title = {An upper bound on the reduction number of an ideal},
author = {Yayoi Kinoshita and Koji Nishida and Kensuke Sakata and Ryuta Shinya},
journal= {arXiv preprint arXiv:0711.4880},
year = {2007}
}
Comments
9 pages