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Depth and Stanley depth of two special classes of monomial ideals

Xiaoqi Wei
대한수학회 (The Korean Mathematical Society)|2024.01|대한수학회보 (Bulletin of the KMS)|제61권 제1호|pp. 147-160|DOI 10.4134/BKMS.b230066

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키워드

depthMonomial idealStanley depthStanley conjecture
주제분류수학

초록

In this paper, we define two new classes of monomial ideals $I_{l,d}$ and $J_{k,d}$. When $d\geq 2k+1$ and $l\leq d-k-1$, we give the exact formulas to compute the depth and Stanley depth of quotient rings $S/I_{l,d}^{t}$ for all $t\geq 1$. When $d=2k=2l$, we compute the depth and Stanley depth of quotient ring $S/I_{l,d}$. When $d\geq 2k$, we also compute the depth and Stanley depth of quotient ring $S/J_{k,d}$.

Abstract

In this paper, we define two new classes of monomial ideals $I_{l,d}$ and $J_{k,d}$. When $d\geq 2k+1$ and $l\leq d-k-1$, we give the exact formulas to compute the depth and Stanley depth of quotient rings $S/I_{l,d}^{t}$ for all $t\geq 1$. When $d=2k=2l$, we compute the depth and Stanley depth of quotient ring $S/I_{l,d}$. When $d\geq 2k$, we also compute the depth and Stanley depth of quotient ring $S/J_{k,d}$.

참고문헌 (19)

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