半群CSPO_n中星理想的秩和相关秩

On the Rank and Relative Rank of Each Star Ideal of the Semigroup CSPO_n

设自然数n≥4，CSPOn是有限链[n]上的严格部分保序且压缩奇异变换半群．对任意的r（0≤r≤n-1），记N P＊（n，r）={α∈CSPOn：｜Im（α）｜≤r）为半群CSPOn的双边星理想．通过对秩为r的元素和星格林关系的分析，分别获得了半群N P＊（n，r）的极小生成集和秩．进一步确定了当0≤l≤r时，半群N P＊（n，r）关于其星理想N P＊（n，l）的相关秩．

Let CSPO n be the semigroup of all strictly partial order-preserving and compressing singular transformations on a finite-chain [n] if n ≥ 4, and let N P＊（n,r） = {α ∈ CSPOn ： ｜Im（α） ｜≤ r） be the two-sided star ideal of the semigroup CSPOn if for an arbitrary integer r such that 0 ≤ r ≤ n - 1. By analyzing the elements of rank r and star Green＇s relations, the minimal generating set and rank of the semigroup N P＊ （n, r） are obtained, respectively. Furthermore, the relative rank of the semigroup N P＊（n, r） with respect to itself each star ideal N P（n, l） is determined if 0 ≤ l ≤ r.