On the Rank of the Certain Orthodox Semigroups
Gao Rong-hai · Journal of South China Normal University · 2013
Let Xn = { 1,2,…,n}(n≥4) be natural order set,Wn be semigroup of the order-preserving and compressing singular transformations on Xn,RWn be regular subsemigroup consisting of all regular elements in Wn.By Green equivalence and eggbox graph,it is shown that the rank of ideals Ir = { α RWn: im α ≤r}(1≤r≤n 1) be n-r + 1.