关于一类纯正半群的秩

On the rank of the certain orthodox semigroups

摘要: 设~X_n=\1, 2,\ldots, n\(n \geq 4) 是一个自然序集,W_n 是~X_n 上的保序压缩奇异变换半群,RW_n是W_n的所有正则元构成的正则子半群.利用Green等价关系和蛋合图，证明了RW_n的理想I_r=\\alpha\in RW_n:\mid im \alpha\mid\leq r\(1\leq r\leq n-1) 秩为n-r+1.

Abstract: Let X_n=\1, 2, \ldots, n\(n\geq 4) be natural order set,W_n be semigroup of the order-preserving and compressing singular transformations on X_n,RW_n be regular subsemigroup consisting of all regular elements in W_n.By Green equivalence and eggbox graph,we obtained that rank of ideals I_r =\\alpha\in RW_n:\mid im \alpha\mid\leq r\(1\leq r\leq n-1) be n-r+1 .