Journal of Commutative Algebra

Stanley conjecture on monomial ideals of mixed products

Gaetana Restuccia, Zhongming Tang, and Rosanna Utano

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Abstract

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

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

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jca/1425307759

Digital Object Identifier
doi:10.1216/JCA-2015-7-1-77

Mathematical Reviews number (MathSciNet)
MR3316986

Zentralblatt MATH identifier
1322.13006

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

Citation

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. https://projecteuclid.org/euclid.jca/1425307759


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