Geodesic
On Stanley Depths of Certain Monomial Factor Algebras
Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 393-401

Voir la notice de l'article provenant de la source Cambridge University Press

Let $S\,=\,K\left[ {{x}_{1}},\,\ldots \,,\,{{x}_{n}} \right]$ be the polynomial ring in $n$ -variables over a field $K$ and $I$ a monomial ideal of $S$ . According to one standard primary decomposition of $I$ , we get a Stanley decomposition of the monomial factor algebra $S/I$ . Using this Stanley decomposition, one can estimate the Stanley depth of $S/I$ . It is proved that $\text{sdept}{{\text{h}}_{s}}\left( S/I \right)\,\ge \,\text{siz}{{\text{e}}_{S}}\left( I \right)$ . When $I$ is squarefree and $\text{bigsiz}{{\text{e}}_{S}}\left( I \right)\,\le \,2$ , the Stanley conjecture holds for $S/I$ , i.e., $\text{sdept}{{\text{h}}_{S}}\left( S/I \right)\ge \text{dept}{{\text{h}}_{S}}\left( S/I \right)$ .
DOI : 10.4153/CMB-2015-001-x
Mots-clés : 13F20, 13C15, monomial, ideal size, Stanley depth 
Tang, Zhongming. On Stanley Depths of Certain Monomial Factor Algebras. Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 393-401. doi: 10.4153/CMB-2015-001-x
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[1] [1] Cimpoeas, C., Some remarks on the Stanley depth for multigraded modules. Matematiche (Catania) 63 (2008), no. 2,165–171. Google Scholar

[2] [2] Herzog, J., Jahan, A. S., and X. Zheng, Skeletons of monomial ideals. Math. Nachr. 283 (2010), no. 10, 1403–1408. http://dx.doi.Org/10.1OO2/mana.2OO810039 Google Scholar

[3] [3] Herzog, J., Popescu, D., and Vadoiu, M., Stanley depth and size of a monomial ideal. Proc. Amer. Math. Soc. 140 (2012), no. 2, 493–504. Google Scholar | DOI

[4] [4] Ichim, B., Katthan, L., and Moyano-Fernandez, J. J., The behavior of Stanley depth under polarization. arxiv:1401.4309 Google Scholar

[5] [5] Lyubeznik, G., On the arithmetical rank of monomial ideals. J. Algebra, 112 (1988), no. 1, 86–89. http://dx.doi.Org/10.1016/0021-8693(88)90133–0 Google Scholar

[6] [6] Popescu, A., Special Stanley decompositions. Bull. Math. Soc. Sci. Math. Roumanie 53 (101)(2010), no. 4, 363–372. Google Scholar

[7] [7] Popescu, A., The Stanley conjecture on intersections of four monomial prime ideals. Comm. Algebra 41 (2013), no. 11,4351–4362. Google Scholar | DOI

[8] [8] Popescu, A., Graph and depth of a monomial squarefree ideal. Proc. Amer. Math. Soc. 140 (2012), no. 11, 3813–3822. Google Scholar | DOI

[9] [9] Popescu, A., Stanley depth of multigraded modules. J. Algebra 321 (2009), no. 10, 2782–2797. http://dx.doi.Org/10.1016/j.jalgebra.2009.03.009 Google Scholar

[10] [10] Popescu, D. and Qureshi, M. I., Computing the Stanley depth. J. Algebra 323 (2010), no. 10, 2943–2959. http://dx.doi.Org/10.1016/j.jalgebra.2009.11.025 Google Scholar

[11] [11] Stanley, R. P., Linear Diophantine equations and local cohomology. Invent. Math. 68 (1982), no. 2, 175–193. Google Scholar | DOI

[12] [12] Tang, Z., Stanley depths of certain Stanley-Reisner rings. J. Algebra 409 (2014), 430–443. Google Scholar | DOI

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