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Stanley depth of monomial ideals with small number of generators

  • Research Article
  • Published:
Central European Journal of Mathematics

Abstract

For a monomial ideal I ⊂ S = K[x 1...,x n ], we show that sdepth(S/I) ≥ n − g(I), where g(I) is the number of the minimal monomial generators of I. If I =νI′, where ν ∈ S is a monomial, then we see that sdepth(S/I) = sdepth(S/I′). We prove that if I is a monomial ideal I ⊂ S minimally generated by three monomials, then I and S/I satisfy the Stanley conjecture. Given a saturated monomial ideal I ⊂ K[x 1,x 2,x 3] we show that sdepth(I) = 2. As a consequence, sdepth(I) ≥ sdepth(K[x 1,x 2,x 3]//I) +1 for any monomial ideal in I ⊂ K[x 1,x 2,x 3].

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Authors and Affiliations

  1. Institute of Mathematics of the Romanian Academy, Bucharest, Romania

    Mircea Cimpoeaş

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  1. Mircea Cimpoeaş
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Correspondence to Mircea Cimpoeaş.

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Cimpoeaş, M. Stanley depth of monomial ideals with small number of generators. centr.eur.j.math. 7, 629–634 (2009). https://doi.org/10.2478/s11533-009-0037-0

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  • DOI: https://doi.org/10.2478/s11533-009-0037-0

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