半群W_n^-中星理想的相关秩

On the Relative Rank of Each Star Ideal of the Semigroup W_n^-

设自然数n≥3,Wn-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 ＆lt; r.