Bull. Korean Math. Soc. 2024; 61(1): 147-160
Online first article January 17, 2024 Printed January 31, 2024
https://doi.org/10.4134/BKMS.b230066
Copyright © The Korean Mathematical Society.
Xiaoqi Wei
Jiangsu University of Technology
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 $S/J_{k,d}$.
Keywords: Monomial ideal, depth, Stanley depth, Stanley conjecture
MSC numbers: 13C15, 13P10, 13F20, 13F55
Supported by: This work was supported by the National Natural Science Foundation of China (No. 12126330).
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