English

Colength, multiplicity, and ideal closure operations

Commutative Algebra 2023-01-10 v4

Abstract

In a formally unmixed Noetherian local ring, if the colength and multiplicity of an integrally closed ideal agree, then RR is regular. We deduce this using the relationship between multiplicity and various ideal closure operations.

Keywords

Cite

@article{arxiv.1907.00951,
  title  = {Colength, multiplicity, and ideal closure operations},
  author = {Linquan Ma and Pham Hung Quy and Ilya Smirnov},
  journal= {arXiv preprint arXiv:1907.00951},
  year   = {2023}
}

Comments

7 pages, final version. A small inaccuracy in the proof of Lemma 4 is fixed

R2 v1 2026-06-23T10:09:06.251Z