On Stanley Depths of Certain Monomial Factor Algebras

Canadian mathematical bulletin

Zhongming Tang¹ 

[1] Department of Mathematics, Suzhou University, Suzhou 215006, PR~China

关键词: monomial ideal;    size;    Stanley depth;   

DOI  :  10.4153/CMB-2015-001-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $S=K[x_1,ldots,x_n]$be the polynomialring in $n$-variables over a field $K$ and $I$ a monomial idealof $S$. 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 Stanleydepth of $S/I$. It is proved that${operatorname {sdepth}}_S(S/I)geq{operatorname {size}}_S(I)$. When $I$ is squarefree and ${operatorname {bigsize}}_S(I)leq 2$, the Stanley conjecture holdsfor$S/I$, i.e., ${operatorname {sdepth}}_S(S/I)geq{operatorname {depth}}_S(S/I)$.

【 授权许可】

Unknown