Free resolutions of lex-ideals over a koszul toric ring

Satoshi Murai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this paper, we study the minimal free resolution of lex-ideals over a Koszul toric ring. In particular, we study in which toric ring R all lexidealsare componentwise linear. We give a certain necessity and sufficiency condition for this property, and show that lex-ideals in a strongly Koszul toric ring are componentwise linear. In addition, it is shown that, in the toric ring arising from the Segre product 1 × ⋯ ×1, every Hilbert function of a graded ideal is attained by a lex-ideal and that lex-ideals have the greatest graded Betti numbers among all ideals having the same Hilbert function.

Original languageEnglish
Pages (from-to)857-885
Number of pages29
JournalTransactions of the American Mathematical Society
Issue number2
Publication statusPublished - 2011 Feb
Externally publishedYes


  • Componentwise linear ideals
  • Free resolutions
  • Hilbert functions
  • Koszul algebras
  • Lex-ideals
  • Toric rings

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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