设自然数 n≥3，W -n 是有限链[n]上具有降序性的保序且压缩奇异变换半群，对任意的 r（1≤r≤n -1），记 K*-（n，r）=｛α∈W -n ：| Imα|≤r｝为半群 W -n 的双边星理想。通过对秩为 r 的元素和星格林关系的分析，确定了当1≤l ＜ r 时，半群 K*-（n，r）关于其星理想 K*-（n，l）的相关秩。%Let W be the semigroup of all order-preserving and compressing singular transformations with decreasing on a finite-chain[n]if n≥3,and let K(n,r)={α∈W:| Imα| ≤r}be the two-sided star ideal of the semigroups W for an arbitrary integer r if 1≤r≤n - 1. By analyzing the elements of rank r and star Greenˊs relations,the relative rank of the semigroups K(n,r)with respect to itself each star ideal K(n,r)is determined if 1≤l < r.
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