Freiman ideals and the number of generators of powers of monomial ideals

Ibrahim Al-Ayyoub*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let lðIÞ denote the number of generators of a monomial ideal I. It is well
known that lðI
kÞ < lðI
kþ1Þ for k 0: In this paper we construct monomial
ideals I in F½x, y such that lðI
kþ1Þ < lðI
kÞ for all k l, given any positive
integer l. Also, we extend some results of Eliahou et al. by constructing
monomial ideals in R ¼ F½x1, :::, xn with lðI
2Þ < lðIÞ and investigate lðI

for monomial ideals in R. Furthermore, we generalize the definition of
Freiman ideals given in Herzog and Zhu and extend some results with simpler proofs. In particular, we give a complete characterization of Freiman
ideals of maximum height in R
Original languageEnglish
Pages (from-to)877-891
Number of pages15
JournalCommunications in Algebra
Issue number2
Publication statusPublished - 2021

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