Arithmetical rank of squarefree monomial ideals of small arithmetic degree

Kyouko Kimura, Naoki Terai, Ken Ichi Yoshida

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


In this paper, we prove that the arithmetical rank of a squarefree monomial ideal I is equal to the projective dimension of R/I in the following cases: (a) I is an almost complete intersection; (b) arithdeg∈I=reg∈I; (c) arithdeg∈I=indeg∈I+1. We also classify all almost complete intersection squarefree monomial ideals in terms of hypergraphs, and use this classification in the proof in case (c).

Original languageEnglish
Pages (from-to)389-404
Number of pages16
JournalJournal of Algebraic Combinatorics
Issue number3
Publication statusPublished - May 2009
Externally publishedYes


  • Alexander duality
  • Almost complete intersection
  • Arithmetic degree
  • Arithmetical rank
  • Initial degree
  • Regularity

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics


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