English

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.

Keywords

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

R2 v1 2026-06-21T09:48:56.601Z