Remarks on the Stanley depth and Hilbert depth of monomial ideals with linear quotients
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| Format: | Preprint |
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2021
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| _version_ | 1866914794581262336 |
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| author | Bordianu, Andreea I. Cimpoeas, Mircea |
| author_facet | Bordianu, Andreea I. Cimpoeas, Mircea |
| contents | We prove that if $I$ is a monomial ideal with linear quotients in a ring of polynomials $S$ in $n$ indeterminates and $\operatorname{depth}(S/I)=n-2$, then $\operatorname{sdepth}(S/I)=n-2$ and, if $I$ is squarefree, $\operatorname{hdepth}(S/I)=n-2$.
Also, we prove that $\operatorname{sdepth}(S/I)\geq \operatorname{depth}(S/I)$ for a monomial ideal $I$ with linear quotients which satisfies certain technical conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_07196 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Remarks on the Stanley depth and Hilbert depth of monomial ideals with linear quotients Bordianu, Andreea I. Cimpoeas, Mircea Commutative Algebra 05E40, 06A17, 13A15, 13C15, 13P10 We prove that if $I$ is a monomial ideal with linear quotients in a ring of polynomials $S$ in $n$ indeterminates and $\operatorname{depth}(S/I)=n-2$, then $\operatorname{sdepth}(S/I)=n-2$ and, if $I$ is squarefree, $\operatorname{hdepth}(S/I)=n-2$. Also, we prove that $\operatorname{sdepth}(S/I)\geq \operatorname{depth}(S/I)$ for a monomial ideal $I$ with linear quotients which satisfies certain technical conditions. |
| title | Remarks on the Stanley depth and Hilbert depth of monomial ideals with linear quotients |
| topic | Commutative Algebra 05E40, 06A17, 13A15, 13C15, 13P10 |
| url | https://arxiv.org/abs/2102.07196 |