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## Open Mathematics

2009 | 7 | 4 | 629-634
Tytuł artykułu

### Stanley depth of monomial ideals with small number of generators

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EN
Abstrakty
EN
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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EN
Kategorie tematyczne
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Tom
Numer
Strony
629-634
Opis fizyczny
Daty
wydano
2009-12-01
online
2009-10-31
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autor
Bibliografia
• [1] Ahmad S., Popescu D., Sequentially Cohen-Macaulay monomial ideals of embedding dimension four, Bull. Math. Soc. Sci. Math. Roumanie, 2007, 50(98), 99–110
• [2] Anwar I., Janet’s algorithm, Bull. Math. Soc. Sci. Math. Roumanie, 2008, 51(99), 11–19
• [3] Anwar I., Popescu D., Stanley Conjecture in small embedding dimension, J. Algebra, 2007, 318, 1027–1031 http://dx.doi.org/10.1016/j.jalgebra.2007.06.005[Crossref][WoS]
• [4] Apel J., On a conjecture of R.P.Stanley, J. Algebraic Combin., 2003, 17, 36–59
• [5] Cimpoeas M., Stanley depth for monomial complete intersection, Bull. Math. Soc. Sci. Math. Roumanie, 2008, 51(99), 205–211
• [6] Cimpoeas M., Some remarks on the Stanley depth for multigraded modules, Le Mathematiche, 2008, LXIII, 165–171
• [7] Herzog J., Jahan A.S., Yassemi S., Stanley decompositions and partitionable simplicial complexes, J. Algebraic Combin., 2008, 27, 113–125 http://dx.doi.org/10.1007/s10801-007-0076-1[Crossref]
• [8] Herzog J., Vladoiu M., Zheng X., How to compute the Stanley depth of a monomial ideal, J. Algebra, doi:10:1016/j.jalgebra.2008.01.006, to appear [WoS]
• [9] Jahan A.S., Prime filtrations of monomial ideals and polarizations, J. Algebra, 2007, 312, 1011–1032 http://dx.doi.org/10.1016/j.jalgebra.2006.11.002[Crossref]
• [10] Nasir S., Stanley decompositions and localization, Bull. Math. Soc. Sci. Math. Roumanie, 2008, 51(99), 151–158
• [11] Popescu D., Stanley depth of multigraded modules, J. Algebra, 2009, 321(10), 2782–2797 http://dx.doi.org/10.1016/j.jalgebra.2009.03.009[Crossref][WoS]
• [12] Rauf A., Stanley decompositions, pretty clean filtrations and reductions modulo regular elements, Bull. Soc. Sci. Math. Roumanie, 2007, 50(98), 347–354
• [13] Rauf A., Depth and Stanley depth of multigraded modules, Comm. Algebra, to appear
• [14] Shen Y., Stanley depth of complete intersection monomial ideals and upper-discrete partitions, J. Algebra, 2009, 321, 1285–1292 http://dx.doi.org/10.1016/j.jalgebra.2008.11.010[WoS][Crossref]
Typ dokumentu
Bibliografia
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