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Lobachevskii Journal of Mathematics

, Volume 40, Issue 1, pp 85–89 | Cite as

Monomial Ideals with Quasi-Linear Quotients

  • S. NazirEmail author
  • I. AnwarEmail author
  • A. AhmadEmail author
Article
  • 2 Downloads

Abstract

In this paper, we extend the notion of quasi-linear quotients for a pure monomial ideal (not necessarily square-free) of degree d. We introduce the notion of quasi-linear free resolution and show that if a pure monomial ideal I = (u1, u2,…, um) of degree d in the polynomial ring S = k[x1,…, xn] admits quasi-linear quotients then Lq = (u1,…, uq−1): uq admits quasi-linear free resolution for all qm. Moreover, we show that if a pure monomial ideal I of degree d admits quasi-linear quotients then It will also have quasi-linear quotients for td.

Keywords and phrases

shellable simplicial complex facet ideal graded free resolution graded betti numbers betti diagram colon of monomial ideals 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lahore University of Management SciencesLahore, PunjabPakistan
  2. 2.Abdus Salam School ofMathematical SciencesGC UniversityLahorePakistan
  3. 3.COMSATS Institute of Information TechnologyLahore, PunjabPakistan

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