On the Rank and Idempotent Rank of Each Star Ideal of the Semigroup H_n
Luo Yong-gu · Journal of Sichuan Normal University · 2014
Let H n be the semigroups of order-decreasing and order-preserving finite singular transformations on the natural order set X n = { 1,2,3,…,n}( n≥3),and let H( n,r) = { α∈H n :|Im α|≤r} be the two-sided star ideal of the semigroup H n.In this paper,the semigroup H( n,r) generated by idempotents of rank r is characterized,and we proved that its rank and idempotent rank are both equal to Cr- 1 n- 1 if 1≤r≤n- 1.Furthermore,it is shown that r( H( n,r),H( n,l)) is 0 if l = r or is Cr- 1 n- 1 if 1≤l r.