English

Multiplicity sequence and integral dependence

Commutative Algebra 2021-10-18 v1

Abstract

We prove that two arbitrary ideals IJI \subset J in an equidimensional and universally catenary Noetherian local ring have the same integral closure if and only if they have the same multiplicity sequence. We also obtain a Principle of Specialization of Integral Dependence, which gives a condition for integral dependence in terms of the constancy of the multiplicity sequence in families.

Keywords

Cite

@article{arxiv.2008.00384,
  title  = {Multiplicity sequence and integral dependence},
  author = {Claudia Polini and Ngo Viet Trung and Bernd Ulrich and Javid Validashti},
  journal= {arXiv preprint arXiv:2008.00384},
  year   = {2021}
}

Comments

17 pages, to be published in Math. Ann

R2 v1 2026-06-23T17:34:47.012Z