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On Stanley Depths of Certain Monomial Factor Algebras

Published online by Cambridge University Press:  20 November 2018

Zhongming Tang
Zhongming Tang*
Affiliation:
Department of Mathematics, Suzhou University, Suzhou 215006, PR China. e-mail: [email protected]
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Abstract

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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., $\text{sdept}{{\text{h}}_{S}}\left( S/I \right)\ge \text{dept}{{\text{h}}_{S}}\left( S/I \right)$.

Keywords

13F2013C15monomialideal sizeStanley depth
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 2 , 01 June 2015 , pp. 393 - 401
Copyright
Copyright © Canadian Mathematical Society 2015

References

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