Stanley depth of monomial ideals with small number of generators

Mircea Cimpoeaş

Open Mathematics (2009)

  • Volume: 7, Issue: 4, page 629-634
  • ISSN: 2391-5455

Abstract

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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].

How to cite

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Mircea Cimpoeaş. "Stanley depth of monomial ideals with small number of generators." Open Mathematics 7.4 (2009): 629-634. <http://eudml.org/doc/269496>.

@article{MirceaCimpoeaş2009,
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].},
author = {Mircea Cimpoeaş},
journal = {Open Mathematics},
keywords = {Stanley depth; Monomial ideal; monomial ideal},
language = {eng},
number = {4},
pages = {629-634},
title = {Stanley depth of monomial ideals with small number of generators},
url = {http://eudml.org/doc/269496},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Mircea Cimpoeaş
TI - Stanley depth of monomial ideals with small number of generators
JO - Open Mathematics
PY - 2009
VL - 7
IS - 4
SP - 629
EP - 634
AB - 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].
LA - eng
KW - Stanley depth; Monomial ideal; monomial ideal
UR - http://eudml.org/doc/269496
ER -

References

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