Journal of Commutative Algebra

Stanley conjecture on monomial ideals of mixed products

Gaetana Restuccia, Zhongming Tang, and Rosanna Utano

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


It is proved that the Stanley conjecture holds for monomial ideals of mixed products, i.e., if $I$ is an ideal of mixed products in a polynomial ring $S$ over a field, then ${\rm sdepth}_S(I) \geq {\rm depth}_S(I)$ and ${\rm sdepth}_S(S/I) \geq {\rm depth}_S(S/I)$.

Article information

J. Commut. Algebra, Volume 7, Number 1 (2015), 77-88.

First available in Project Euclid: 2 March 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13C15: Dimension theory, depth, related rings (catenary, etc.) 13F20: Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]


Restuccia, Gaetana; Tang, Zhongming; Utano, Rosanna. Stanley conjecture on monomial ideals of mixed products. J. Commut. Algebra 7 (2015), no. 1, 77--88. doi:10.1216/JCA-2015-7-1-77.

Export citation


  • W. Bruns and J. Herzog, Cohen-Macaulay rings, Cambridge University Press, Cambridge, 1997.
  • M. Cimpoeas, Several inequalities regarding Stanley depth, Roum. J. Math. Comp. Sci. 2 (2012), 28–40.
  • J. Herzog, D. Popescu and M. Vladoiu, Stanley depth and size of a monomial ideal, Proc. Amer. Math. Soc. 140 (2012), 493–504.
  • J. Herzog, M. Vladoiu and X. Zheng, How to compute the Stanley depth of a monomial ideal, J. Alg. 322 (2009), 3151–3169.
  • C. Ionescu and G. Rinaldo, Some algebraic invariants related to mixed product ideals, Arch. Math. 91 (2008), 20–30.
  • M. Ishaq, Values and bounds of the Stanley depth, Carpathian J. Math. 27 (2011), 217–224.
  • A. Popescu, Special Stanley decompositions, Bull. Math. Soc. Sci. Math. Roum. 53 (2010), 363–372.
  • D. Popescu, An inequality between depth and Stanley depth, Bull. Math. Soc. Sci. Math. Roum. 52 (2009), 377–382.
  • ––––, Stanley depth of multigraded modules, J. Alg. 321 (2009), 2782–2797.
  • ––––, Stanley conjecture on intersections of four monomial prime ideals, Comm. Alg. 41 (2013), 4351–4362.
  • A. Rauf, Depth and Stanley depth of multigraded module, Comm. Alg. 38 (2010), 773–784.
  • G. Restuccia and R. Villarreal, On the normality of monomial ideals of mixed products, Comm. Alg. 29 (2001), 3571–3580.
  • R.P. Stanley, Linear Diophantine equations and local cohomology, Invent. Math. 68 (1982), 175–193.
  • Z. Tang, Stanley depths of certain Stanley-Reisner rings, J. Alg. 409 (2014), 430–443.
  • R.H. Villarreal, Monomial algebras, Dekker, New York, 2001.