Colength, multiplicity, and ideal closure operations

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

Saved in:
Bibliographic Details
Published inCommunications in algebra Vol. 48; no. 4; pp. 1601 - 1607
Main Authors Ma, Linquan, Quy, Pham Hung, Smirnov, Ilya
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.04.2020
Taylor & Francis Ltd
Subjects
Hilbert-Samuel multiplicity
integral closure
limit closure
Primary 13H15
Secondary 13A35
Online AccessGet full text

Cover

More Information
Summary:In a formally unmixed Noetherian local ring, if the colength and multiplicity of an integrally closed ideal agree, then R is regular. We deduce this using the relationship between multiplicity and various ideal closure operations.
ISSN:0092-7872
1532-4125
1532-4125
DOI:10.1080/00927872.2019.1691577